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Sample records for gravity noncommutative geometry

Modular Theory, Non-Commutative Geometry and Quantum Gravity

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Wicharn Lewkeeratiyutkul

2010-08-01

Full Text Available This paper contains the first written exposition of some ideas (announced in a previous survey on an approach to quantum gravity based on Tomita-Takesaki modular theory and A. Connes non-commutative geometry aiming at the reconstruction of spectral geometries from an operational formalism of states and categories of observables in a covariant theory. Care has been taken to provide a coverage of the relevant background on modular theory, its applications in non-commutative geometry and physics and to the detailed discussion of the main foundational issues raised by the proposal.
Noncommutative geometry inspired black holes in Rastall gravity

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Ma, Meng-Sen [Shanxi Datong University, Institute of Theoretical Physics, Datong (China); Shanxi Datong University, Department of Physics, Datong (China); Zhao, Ren [Shanxi Datong University, Institute of Theoretical Physics, Datong (China)

2017-09-15

Under two different metric ansatzes, the noncommutative geometry inspired black holes (NCBH) in the framework of Rastall gravity are derived and analyzed. We consider the fluid-type matter with the Gaussian-distribution smeared mass density. Taking a Schwarzschild-like metric ansatz, it is shown that the noncommutative geometry inspired Schwarzschild black hole (NCSBH) in Rastall gravity, unlike its counterpart in general relativity (GR), is not a regular black hole. It has at most one event horizon. After showing a finite maximal temperature, the black hole will leave behind a point-like massive remnant at zero temperature. Considering a more general metric ansatz and a special equation of state of the matter, we also find a regular NCBH in Rastall gravity, which has a similar geometric structure and temperature to that of NCSBH in GR. (orig.)
Intersecting Quantum Gravity with Noncommutative Geometry - a Review

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Johannes Aastrup

2012-03-01

Full Text Available We review applications of noncommutative geometry in canonical quantum gravity. First, we show that the framework of loop quantum gravity includes natural noncommutative structures which have, hitherto, not been explored. Next, we present the construction of a spectral triple over an algebra of holonomy loops. The spectral triple, which encodes the kinematics of quantum gravity, gives rise to a natural class of semiclassical states which entail emerging fermionic degrees of freedom. In the particular semiclassical approximation where all gravitational degrees of freedom are turned off, a free fermionic quantum field theory emerges. We end the paper with an extended outlook section.
PREFACE: Conceptual and Technical Challenges for Quantum Gravity 2014 - Parallel session: Noncommutative Geometry and Quantum Gravity

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Martinetti, P.; Wallet, J.-C.; Amelino-Camelia, G.

2015-08-01

The conference Conceptual and Technical Challenges for Quantum Gravity at Sapienza University of Rome, from 8 to 12 September 2014, has provided a beautiful opportunity for an encounter between different approaches and different perspectives on the quantum-gravity problem. It contributed to a higher level of shared knowledge among the quantum-gravity communities pursuing each specific research program. There were plenary talks on many different approaches, including in particular string theory, loop quantum gravity, spacetime noncommutativity, causal dynamical triangulations, asymptotic safety and causal sets. Contributions from the perspective of philosophy of science were also welcomed. In addition several parallel sessions were organized. The present volume collects contributions from the Noncommutative Geometry and Quantum Gravity parallel session4, with additional invited contributions from specialists in the field. Noncommutative geometry in its many incarnations appears at the crossroad of many researches in theoretical and mathematical physics: • from models of quantum space-time (with or without breaking of Lorentz symmetry) to loop gravity and string theory, • from early considerations on UV-divergencies in quantum field theory to recent models of gauge theories on noncommutative spacetime, • from Connes description of the standard model of elementary particles to recent Pati-Salam like extensions. This volume provides an overview of these various topics, interesting for the specialist as well as accessible to the newcomer. 4partially funded by CNRS PEPS /PTI ''Metric aspect of noncommutative geometry: from Monge to Higgs''
Beyond the Standard Model with noncommutative geometry, strolling towards quantum gravity

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Martinetti, Pierre

2015-01-01

Noncommutative geometry in its many incarnations appears at the crossroad of many researches in theoretical and mathematical physics: from models of quantum spacetime(with or without breaking of Lorentz symmetry) to loop gravity and string theory, from early considerations on UV-divergenciesin quantum field theory to recent models of gauge theories on noncommutatives pacetime, from Connes description of the standard model of elementary particles to recent Pati-Salam like extensions. We list several of these applications, emphasizing also the original point of view brought by noncommutative geometry on the nature of time. This text serves as an introduction to the volume of proceedings of the parallel session “Noncommutative geometry and quantum gravity”, as a part of the conference “Conceptual and technical challenges in quantum gravity” organized at the University of Rome La Sapienza sin September 2014. (paper)
Noncommutative gravity

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Schupp, P.

2007-01-01

Heuristic arguments suggest that the classical picture of smooth commutative spacetime should be replaced by some kind of quantum / noncommutative geometry at length scales and energies where quantum as well as gravitational effects are important. Motivated by this idea much research has been devoted to the study of quantum field theory on noncommutative spacetimes. More recently the focus has started to shift back to gravity in this context. We give an introductory overview to the formulation of general relativity in a noncommutative spacetime background and discuss the possibility of exact solutions. (author)
Quantum gravity from noncommutative spacetime

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Lee, Jungjai [Daejin University, Pocheon (Korea, Republic of); Yang, Hyunseok [Korea Institute for Advanced Study, Seoul (Korea, Republic of)

2014-12-15

We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative *-algebra) of quantum gravity.
Quantum gravity from noncommutative spacetime

International Nuclear Information System (INIS)

Lee, Jungjai; Yang, Hyunseok

2014-01-01

We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative *-algebra) of quantum gravity.
Noncommutative Geometry, Quantum Fields and Motives

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Connes, Alain

2007-01-01

The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book dea
Entropic force, noncommutative gravity, and ungravity

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Nicolini, Piero

2010-01-01

After recalling the basic concepts of gravity as an emergent phenomenon, we analyze the recent derivation of Newton's law in terms of entropic force proposed by Verlinde. By reviewing some points of the procedure, we extend it to the case of a generic quantum gravity entropic correction to get compelling deviations to the Newton's law. More specifically, we study: (1) noncommutative geometry deviations and (2) ungraviton corrections. As a special result in the noncommutative case, we find that the noncommutative character of the manifold would be equivalent to the temperature of a thermodynamic system. Therefore, in analogy to the zero temperature configuration, the description of spacetime in terms of a differential manifold could be obtained only asymptotically. Finally, we extend the Verlinde's derivation to a general case, which includes all possible effects, noncommutativity, ungravity, asymptotically safe gravity, electrostatic energy, and extra dimensions, showing that the procedure is solid versus such modifications.
Arithmetic noncommutative geometry

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Marcolli, Matilde

2005-01-01

Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...
Noncommutative geometry inspired Einstein–Gauss–Bonnet black holes

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Ghosh, Sushant G.

2018-04-01

Low energy limits of a string theory suggests that the gravity action should include quadratic and higher-order curvature terms, in the form of dimensionally continued Gauss–Bonnet densities. Einstein–Gauss–Bonnet is a natural extension of the general relativity to higher dimensions in which the first and second-order terms correspond, respectively, to general relativity and Einstein–Gauss–Bonnet gravity. We obtain five-dimensional (5D) black hole solutions, inspired by a noncommutative geometry, with a static spherically symmetric, Gaussian mass distribution as a source both in the general relativity and Einstein–Gauss–Bonnet gravity cases, and we also analyzes their thermodynamical properties. Owing the noncommutative corrected black hole, the thermodynamic quantities have also been modified, and phase transition is shown to be achievable. The phase transitions for the thermodynamic stability, in both the theories, are characterized by a discontinuity in the specific heat at r_+=rC , with the stable (unstable) branch for r ) rC . The metric of the noncommutative inspired black holes smoothly goes over to the Boulware–Deser solution at large distance. The paper has been appended with a calculation of black hole mass using holographic renormalization.
Noncommutative gravity and quantum field theory on noncummutative curved spacetimes

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Schenkel, Alexander

2011-01-01

The purpose of the first part of this thesis is to understand symmetry reduction in noncommutative gravity, which then allows us to find exact solutions of the noncommutative Einstein equations. We propose an extension of the usual symmetry reduction procedure, which is frequently applied to the construction of exact solutions of Einstein's field equations, to noncommutative gravity and show that this leads to preferred choices of noncommutative deformations of a given symmetric system. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models, for which the noncommutative metric field coincides with the classical one. In the second part we focus on quantum field theory on noncommutative curved spacetimes. We develop a new formalism by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. The result is an algebra of observables for scalar quantum field theories on a large class of noncommutative curved spacetimes. A precise relation to the algebra of observables of the corresponding undeformed quantum field theory is established. We focus on explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories, which is not the case in the simplest example of the Moyal-Weyl deformed Minkowski spacetime. The convergent deformation of simple toy-models is investigated and it is shown that these quantum field theories have many new features compared to formal deformation quantization. In addition to the expected nonlocality, we obtain that the relation between the deformed and the undeformed quantum field theory is affected in a nontrivial way, leading to an improved behavior of the noncommutative
Noncommutative gravity and quantum field theory on noncummutative curved spacetimes

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Schenkel, Alexander

2011-10-24

The purpose of the first part of this thesis is to understand symmetry reduction in noncommutative gravity, which then allows us to find exact solutions of the noncommutative Einstein equations. We propose an extension of the usual symmetry reduction procedure, which is frequently applied to the construction of exact solutions of Einstein's field equations, to noncommutative gravity and show that this leads to preferred choices of noncommutative deformations of a given symmetric system. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models, for which the noncommutative metric field coincides with the classical one. In the second part we focus on quantum field theory on noncommutative curved spacetimes. We develop a new formalism by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. The result is an algebra of observables for scalar quantum field theories on a large class of noncommutative curved spacetimes. A precise relation to the algebra of observables of the corresponding undeformed quantum field theory is established. We focus on explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories, which is not the case in the simplest example of the Moyal-Weyl deformed Minkowski spacetime. The convergent deformation of simple toy-models is investigated and it is shown that these quantum field theories have many new features compared to formal deformation quantization. In addition to the expected nonlocality, we obtain that the relation between the deformed and the undeformed quantum field theory is affected in a nontrivial way, leading to an improved behavior of the
Fermions in noncommutative emergent gravity

International Nuclear Information System (INIS)

Klammer, D.

2010-01-01

Noncommutative emergent gravity is a novel framework disclosing how gravity is contained naturally in noncommutative gauge theory formulated as a matrix model. It describes a dynamical space-time which itself is a four-dimensional brane embedded in a higher-dimensional space. In noncommutative emergent gravity, the metric is not a fundamental object of the model; rather it is determined by the Poisson structure and by the induced metric of the embedding. In this work the coupling of fermions to these matrix models is studied from the point of view of noncommutative emergent gravity. The matrix Dirac operator as given by the IKKT matrix model defines an appropriate coupling for fermions to an effective gravitational metric of noncommutative four-dimensional spaces that are embedded into a ten-dimensional ambient space. As it turns out this coupling is non-standard due to a spin connection that vanishes in the preferred but unobservable coordinates defined by the model. The purpose of this work is to study the one-loop effective action of this approach. Standard results of the literature cannot be applied due to this special coupling of the fermions. However, integrating out these fields in a nontrivial geometrical background induces indeed the Einstein-Hilbert action of the effective metric, as well as additional terms which couple the noncommutative structure to the Riemann tensor, and a dilaton-like term. It remains to be understood what the effects of these terms are and whether they can be avoided. In a second step, the existence of a duality between noncommutative gauge theory and gravity which explains the phenomenon of UV/IR mixing as a gravitational effect is discussed. We show how the gravitational coupling of fermions can be interpreted as a coupling of fermions to gauge fields, which suffers then from UV/IR mixing. This explanation does not render the model finite but it reveals why some UV/IR mixing remains even in supersymmetric models, except in the N
Noncommutative geometry and twisted conformal symmetry

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Matlock, Peter

2005-01-01

The twist-deformed conformal algebra is constructed as a Hopf algebra with twisted coproduct. This allows for the definition of conformal symmetry in a noncommutative background geometry. The twisted coproduct is reviewed for the Poincare algebra and the construction is then extended to the full conformal algebra. The case of Moyal-type noncommutativity of the coordinates is considered. It is demonstrated that conformal invariance need not be viewed as incompatible with noncommutative geometry; the noncommutativity of the coordinates appears as a consequence of the twisting, as has been shown in the literature in the case of the twisted Poincare algebra
An invitation to noncommutative geometry

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Marcolli, Matilde

2008-01-01

This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory. Sample Chapter(s). A Walk in the Noncommutative Garden (1,639 KB). Contents: A Walk in the Noncommutative Garden (A Connes & M Marcolli); Renormalization of Noncommutative Quantum Field Theory (H Grosse & R Wulke
Twisted covariant noncommutative self-dual gravity

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Estrada-Jimenez, S.; Garcia-Compean, H.; Obregon, O.; Ramirez, C.

2008-01-01

A twisted covariant formulation of noncommutative self-dual gravity is presented. The formulation for constructing twisted noncommutative Yang-Mills theories is used. It is shown that the noncommutative torsion is solved at any order of the θ expansion in terms of the tetrad and some extra fields of the theory. In the process the first order expansion in θ for the Plebanski action is explicitly obtained.
Computational commutative and non-commutative algebraic geometry

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Cojocaru, S; Ufnarovski, V

2005-01-01

This publication gives a good insight in the interplay between commutative and non-commutative algebraic geometry. The theoretical and computational aspects are the central theme in this study. The topic is looked at from different perspectives in over 20 lecture reports. It emphasizes the current trends in commutative and non-commutative algebraic geometry and algebra. The contributors to this publication present the most recent and state-of-the-art progresses which reflect the topic discussed in this publication. Both researchers and graduate students will find this book a good source of information on commutative and non-commutative algebraic geometry.
Noncommutative geometry

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Connes, Alain

1994-01-01

This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat

Geometry of time-spaces non-commutative algebraic geometry, applied to quantum theory

CERN Document Server

Landau, Olav Arnfinn

2011-01-01

This is a monograph about non-commutative algebraic geometry, and its application to physics. The main mathematical inputs are the non-commutative deformation theory, moduli theory of representations of associative algebras, a new non-commutative theory o
Two lectures on D-geometry and noncommutative geometry

International Nuclear Information System (INIS)

Douglas, M.R.

1999-01-01

This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has appeared in D-brane and Matrix theory physics. (author)
Non-commutative flux representation for loop quantum gravity

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Baratin, A.; Dittrich, B.; Oriti, D.; Tambornino, J.

2011-09-01

The Hilbert space of loop quantum gravity is usually described in terms of cylindrical functionals of the gauge connection, the electric fluxes acting as non-commuting derivation operators. It has long been believed that this non-commutativity prevents a dual flux (or triad) representation of loop quantum gravity to exist. We show here, instead, that such a representation can be explicitly defined, by means of a non-commutative Fourier transform defined on the loop gravity state space. In this dual representation, flux operators act by sstarf-multiplication and holonomy operators act by translation. We describe the gauge invariant dual states and discuss their geometrical meaning. Finally, we apply the construction to the simpler case of a U(1) gauge group and compare the resulting flux representation with the triad representation used in loop quantum cosmology.
On the Generalized Geometry Origin of Noncommutative Gauge Theory

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Jurco, Branislav; Vysoky, Jan

2013-01-01

We discuss noncommutative gauge theory from the generalized geometry point of view. We argue that the equivalence between the commutative and semiclassically noncommutative DBI actions is naturally encoded in the generalized geometry of D-branes.
Finite quantum physics and noncommutative geometry

International Nuclear Information System (INIS)

Balachandran, A.P.; Ercolessi, E.; Landi, G.; Teotonio-Sobrinho, P.; Lizzi, F.; Sparano, G.

1994-04-01

Conventional discrete approximations of a manifold do not preserve its nontrivial topological features. In this article we describe an approximation scheme due to Sorkin which reproduces physically important aspects of manifold topology with striking fidelity. The approximating topological spaces in this scheme are partially ordered sets (posets). Now, in ordinary quantum physics on a manifold M, continuous probability densities generate the commutative C * -algebra C(M) of continuous functions on M. It has a fundamental physical significance, containing the information to reconstruct the topology of M, and serving to specify the domains of observables like the Hamiltonian. For a poset, the role of this algebra is assumed by a noncommutative C * -algebra A. As noncommutative geometries are based on noncommutative C * -algebra, we therefore have a remarkable connection between finite approximations to quantum physics and noncommutative geometries. Varies methods for doing quantum physics using A are explored. Particular attention is paid to developing numerically viable approximation schemes which at the same time preserve important topological features of continuum physics. (author). 21 refs, 13 figs
Index theory for locally compact noncommutative geometries

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Carey, A L; Rennie, A; Sukochev, F A

2014-01-01

Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, the authors prove the local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra. This formula has been successfully used to calculate index pairings in numerous noncommutative examples. The absence of any other effective method of investigating index problems in geometries that are genuinely noncommutative, particularly in the nonunital situation, was a primary motivation for this study and the authors illustrate this point with two examples in the text. In order to understand what is new in their approach in the commutative setting the authors prove an analogue of the Gromov-Lawson relative index formula (for Dirac type operators) for even dimensional manifolds with bounded geometry, without invoking compact supports. For odd dimensional manifolds their index formula appears to be completely new.
Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology & Symplectic Geometry, Noncommutative Geometry and Physics

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Eliashberg, Yakov; Maeda, Yoshiaki; Symplectic, Poisson, and Noncommutative geometry

2014-01-01

Symplectic geometry originated in physics, but it has flourished as an independent subject in mathematics, together with its offspring, symplectic topology. Symplectic methods have even been applied back to mathematical physics. Noncommutative geometry has developed an alternative mathematical quantization scheme based on a geometric approach to operator algebras. Deformation quantization, a blend of symplectic methods and noncommutative geometry, approaches quantum mechanics from a more algebraic viewpoint, as it addresses quantization as a deformation of Poisson structures. This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute: Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology (honoring Alan Weinstein, one of the key figures in the field) and Symplectic Geometry, Noncommutative Geometry and Physics. The chapters include presentations of previously unpublished results and ...
The application of *-products to noncommutative geometry and gauge theory

International Nuclear Information System (INIS)

Sykora, A.

2004-06-01

Due to the singularities arising in quantum field theory and the difficulties in quantizing gravity it is often believed that the description of spacetime by a smooth manifold should be given up at small length scales or high energies. In this work we will replace spacetime by noncommutative structures arising within the framework of deformation quantization. The ordinary product between functions will be replaced by a *-product, an associative product for the space of functions on a manifold. We develop a formalism to realize algebras defined by relations on function spaces. For this purpose we construct the Weyl-ordered *-product and present a method how to calculate *-products with the help of commuting vector fields. Concepts developed in noncommutative differential geometry will be applied to this type of algebras and we construct actions for noncommutative field theories. In the classical limit these noncommutative theories become field theories on manifolds with nonvanishing curvature. It becomes clear that the application of *-products is very fruitful to the solution of noncommutative problems. In the semiclassical limit every *-product is related to a Poisson structure, every derivation of the algebra to a vector field on the manifold. Since in this limit many problems are reduced to a couple of differential equations the *-product representation makes it possible to construct noncommutative spaces corresponding to interesting Riemannian manifolds. Derivations of *-products makes it further possible to extend noncommutative gauge theory in the Seiberg-Witten formalism with covariant derivatives. The resulting noncommutative gauge fields may be interpreted as one forms of a generalization of the exterior algebra of a manifold. For the Formality *-product we prove the existence of the abelian Seiberg-Witten map for derivations of these *-products. We calculate the enveloping algebra valued non abelian Seiberg-Witten map pertubatively up to second order for
Emergent Abelian Gauge Fields from Noncommutative Gravity

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Allen Stern

2010-02-01

Full Text Available We construct exact solutions to noncommutative gravity following the formulation of Chamseddine and show that they are in general accompanied by Abelian gauge fields which are first order in the noncommutative scale. This provides a mechanism for generating cosmological electromagnetic fields in an expanding space-time background, and also leads to multipole-like fields surrounding black holes. Exact solutions to noncommutative Einstein-Maxwell theory can give rise to first order corrections to the metric tensor, as well as to the electromagnetic fields. This leads to first order shifts in the horizons of charged black holes.
On tea, donuts and non-commutative geometry

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Igor V. Nikolaev

2018-03-01

Full Text Available As many will agree, it feels good to complement a cup of tea by a donut or two. This sweet relationship is also a guiding principle of non-commutative geometry known as Serre Theorem. We explain the algebra behind this theorem and prove that elliptic curves are complementary to the so-called non-commutative tori.
Einstein-Podolski-Rosen experiment from noncommutative quantum gravity

International Nuclear Information System (INIS)

Heller, Michael; Sasin, Wieslaw

1998-01-01

It is shown that the Einstein-Podolski-Rosen type experiments are the natural consequence of the groupoid approach to noncommutative unification of general relativity and quantum mechanics. The geometry of this model is determined by the noncommutative algebra A=C c ∞ (G,C) of complex valued, compactly supported, functions (with convolution as multiplication) on the groupoid G=ExΓ. In the model considered in the present paper E is the total space of the frame bundle over space-time and Γ is the Lorentz group. The correlations of the EPR type should be regarded as remnants of the totally non-local physics below the Planck threshold which is modelled by a noncommutative geometry
Introduction to Dubois-Violette's non-commutative differential geometry

International Nuclear Information System (INIS)

Djemai, A.E.F.

1994-07-01

In this work, one presents a detailed review of Dubois-Violette et al. approach to non-commutative differential calculus. The non-commutative differential geometry of matrix algebras and the non-commutative Poisson structures are treated in some details. We also present the analog of the Maxwell's theory and the new models of Yang-Mills-Higgs theories that can be constructed in this framework. In particular, some simple models are compared with the standard model. Finally, we discuss some perspectives and open questions. (author). 32 refs
Non-commutative geometry and supersymmetry 2

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Hussain, F.; Thompson, G.

1991-05-01

Following the general construction of supersymmetric models, the model based on the idea of non-commutative geometry is formulated as a Yang-Mills theory of the graded Lie algebra U(2/1) over a graded space-time manifold. 4 refs
Noncommutative geometry and its application to the standard model

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Martinetti, Pierre [Georg-August Universitaet, Goettingen (Germany)

2009-07-01

We give an overview of the description of the standard model of particle physics minimally coupled to gravity within the framework of noncommutative geometry. Especially we study in detail the metric structure of spacetime that emerges from the spectral triple recently proposed by Chamseddine, Connes and Marcolli. Within this framework points of spacetime acquire an internal structure inherited from the gauge group of the standard model. A distance is defined on this generalized spacetime which is fully encoded by the Yang-Mills gauge fields together with the Higgs field. We focus on some explicit examples, underlying the link between this distance and other distances well known by physicists and mathematicians, such has the Carnot-Caratheodory horizontal distance or the Monge-Kantorovitch transport distance.
A computational non-commutative geometry program for disordered topological insulators

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Prodan, Emil

2017-01-01

This work presents a computational program based on the principles of non-commutative geometry and showcases several applications to topological insulators. Noncommutative geometry has been originally proposed by Jean Bellissard as a theoretical framework for the investigation of homogeneous condensed matter systems. Recently, this approach has been successfully applied to topological insulators, where it facilitated many rigorous results concerning the stability of the topological invariants against disorder. In the first part of the book the notion of a homogeneous material is introduced and the class of disordered crystals defined together with the classification table, which conjectures all topological phases from this class. The manuscript continues with a discussion of electrons’ dynamics in disordered crystals and the theory of topological invariants in the presence of strong disorder is briefly reviewed. It is shown how all this can be captured in the language of noncommutative geometry using the co...
Charged thin-shell gravastars in noncommutative geometry

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Oevguen, Ali [Pontificia Universidad Catolica de Valparaiso, Instituto de Fisica, Valparaiso (Chile); Eastern Mediterranean University, Physics Department, Famagusta, Northern Cyprus (Turkey); Banerjee, Ayan [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India); Jusufi, Kimet [State University of Tetovo, Physics Department, Tetovo (Macedonia, The Former Yugoslav Republic of); Institute of Physics, Ss. Cyril and Methodius University, Faculty of Natural Sciences and Mathematics, Skopje (Macedonia, The Former Yugoslav Republic of)

2017-08-15

In this paper we construct a charged thin-shell gravastar model within the context of noncommutative geometry. To do so, we choose the interior of the nonsingular de Sitter spacetime with an exterior charged noncommutative solution by cut-and-paste technique and apply the generalized junction conditions. We then investigate the stability of a charged thin-shell gravastar under linear perturbations around the static equilibrium solutions as well as the thermodynamical stability of the charged gravastar. We find the stability regions, by choosing appropriate parameter values, located sufficiently close to the event horizon. (orig.)
The local index formula in noncommutative geometry

International Nuclear Information System (INIS)

Higson, N.

2003-01-01

These notes present a partial account of the local index theorem in non-commutative geometry discovered by Alain Connes and Henri Moscovici. It includes Elliptic partial differential operators, cyclic homology theory, Chern characters, homotopy invariants and the index formulas
An introduction to noncommutative spaces and their geometries characterization of the shallow subsurface implications for urban infrastructure and environmental assessment

CERN Document Server

Landi, Giovanni

1997-01-01

These lecture notes are an introduction to several ideas and applications of noncommutative geometry. It starts with a not necessarily commutative but associative algebra which is thought of as the algebra of functions on some 'virtual noncommutative space'. Attention is switched from spaces, which in general do not even exist, to algebras of functions. In these notes, particular emphasis is put on seeing noncommutative spaces as concrete spaces, namely as a collection of points with a topology. The necessary mathematical tools are presented in a systematic and accessible way and include among other things, C'*-algebras, module theory and K-theory, spectral calculus, forms and connection theory. Application to Yang--Mills, fermionic, and gravity models are described. Also the spectral action and the related invariance under automorphism of the algebra is illustrated. Some recent work on noncommutative lattices is presented. These lattices arose as topologically nontrivial approximations to 'contuinuum' topolo...
Non-commutative geometry inspired charged black holes

International Nuclear Information System (INIS)

Ansoldi, Stefano; Nicolini, Piero; Smailagic, Anais; Spallucci, Euro

2007-01-01

We find a new, non-commutative geometry inspired, solution of the coupled Einstein-Maxwell field equations describing a variety of charged, self-gravitating objects, including extremal and non-extremal black holes. The metric smoothly interpolates between de Sitter geometry, at short distance, and Reissner-Nordstrom geometry far away from the origin. Contrary to the ordinary Reissner-Nordstrom spacetime there is no curvature singularity in the origin neither 'naked' nor shielded by horizons. We investigate both Hawking process and pair creation in this new scenario
Minimal length uncertainty and generalized non-commutative geometry

International Nuclear Information System (INIS)

Farmany, A.; Abbasi, S.; Darvishi, M.T.; Khani, F.; Naghipour, A.

2009-01-01

A generalized formulation of non-commutative geometry for the Bargmann-Fock space of quantum field theory is presented. The analysis is related to the symmetry of the simplistic space and a minimal length uncertainty.

Commutative and Non-commutative Parallelogram Geometry: an Experimental Approach

OpenAIRE

Bertram, Wolfgang

2013-01-01

By "parallelogram geometry" we mean the elementary, "commutative", geometry corresponding to vector addition, and by "trapezoid geometry" a certain "non-commutative deformation" of the former. This text presents an elementary approach via exercises using dynamical software (such as geogebra), hopefully accessible to a wide mathematical audience, from undergraduate students and high school teachers to researchers, proceeding in three steps: (1) experimental geometry, (2) algebra (linear algebr...
Non-commutative gauge Gravity: Second- order Correction and Scalar Particles Creation

International Nuclear Information System (INIS)

Zaim, S.

2009-01-01

A noncommutative gauge theory for a charged scalar field is constructed. The invariance of this model under local Poincare and general coordinate transformations is verified. Using the general modified field equation, a general Klein-Gordon equation up to the second order of the noncommu- tativity parameter is derived. As an application, we choose the Bianchi I universe. Using the Seiberg-Witten maps, the deformed noncommutative metric is obtained and a particle production process is studied. It is shown that the noncommutativity plays the same role as an electric field, gravity and chemical potential.
Metric interpretation of gauge fields in noncommutative geometry

International Nuclear Information System (INIS)

Martinetti, P.

2007-01-01

We shall give an overview of the metric interpretation of gauge fields in noncommutative geometry, via Connes distance formula. Especially we shall focus on the Higgs fields in the standard model, and gauge fields in various models of fiber bundle. (author)
Classification of digital affine noncommutative geometries

Science.gov (United States)

Majid, Shahn; Pachoł, Anna

2018-03-01

It is known that connected translation invariant n-dimensional noncommutative differentials dxi on the algebra k[x1, …, xn] of polynomials in n-variables over a field k are classified by commutative algebras V on the vector space spanned by the coordinates. These data also apply to construct differentials on the Heisenberg algebra "spacetime" with relations [xμ, xν] = λΘμν, where Θ is an antisymmetric matrix, as well as to Lie algebras with pre-Lie algebra structures. We specialise the general theory to the field k =F2 of two elements, in which case translation invariant metrics (i.e., with constant coefficients) are equivalent to making V a Frobenius algebra. We classify all of these and their quantum Levi-Civita bimodule connections for n = 2, 3, with partial results for n = 4. For n = 2, we find 3 inequivalent differential structures admitting 1, 2, and 3 invariant metrics, respectively. For n = 3, we find 6 differential structures admitting 0, 1, 2, 3, 4, 7 invariant metrics, respectively. We give some examples for n = 4 and general n. Surprisingly, not all our geometries for n ≥ 2 have zero quantum Riemann curvature. Quantum gravity is normally seen as a weighted "sum" over all possible metrics but our results are a step towards a deeper approach in which we must also "sum" over differential structures. Over F2 we construct some of our algebras and associated structures by digital gates, opening up the possibility of "digital geometry."
Calculating the jet quenching parameter in the plasma of noncommutative Yang-Mills theory from gauge/gravity duality

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Chakraborty, Somdeb; Roy, Shibaji

2012-02-01

A particular decoupling limit of the nonextremal (D1, D3) brane bound state system of type IIB string theory is known to give the gravity dual of space-space noncommutative Yang-Mills theory at finite temperature. We use a string probe in this background to compute the jet quenching parameter in a strongly coupled plasma of hot noncommutative Yang-Mills theory in (3+1) dimensions from gauge/gravity duality. We give expressions for the jet quenching parameter for both small and large noncommutativity. For small noncommutativity, we find that the value of the jet quenching parameter gets reduced from its commutative value. The reduction is enhanced with temperature as T7 for fixed noncommutativity and fixed ’t Hooft coupling. We also give an estimate of the correction due to noncommutativity at the present collider energies like in RHIC or in LHC and find it too small to be detected. We further generalize the results for noncommutative Yang-Mills theories in diverse dimensions.
3D quantum gravity and effective noncommutative quantum field theory.

Science.gov (United States)

Freidel, Laurent; Livine, Etera R

2006-06-09

We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a kappa deformation of the Poincaré group.
Holographic entanglement in a noncommutative gauge theory

International Nuclear Information System (INIS)

Fischler, Willy; Kundu, Arnab; Kundu, Sandipan

2014-01-01

In this article we investigate aspects of entanglement entropy and mutual information in a large-N strongly coupled noncommutative gauge theory, both at zero and at finite temperature. Using the gauge-gravity duality and the Ryu-Takayanagi (RT) prescription, we adopt a scheme for defining spatial regions on such noncommutative geometries and subsequently compute the corresponding entanglement entropy. We observe that for regions which do not lie entirely in the noncommutative plane, the RT-prescription yields sensible results. In order to make sense of the divergence structure of the corresponding entanglement entropy, it is essential to introduce an additional cut-off in the theory. For regions which lie entirely in the noncommutative plane, the corresponding minimal area surfaces can only be defined at this cut-off and they have distinctly peculiar properties
Stability of a non-commutative Jackiw-Teitelboim gravity

Energy Technology Data Exchange (ETDEWEB)

Vassilevich, D.V. [Universitaet Leipzig, Institut fuer Theoretische Physik, Postfach 100 920, Leipzig (Germany); St. Petersburg University, V.A. Fock Institute of Physics, St. Petersburg (Russian Federation); Fresneda, R.; Gitman, D.M. [Sao Paulo Univ. (Brazil). Inst. de Fisica

2006-07-15

We start with a non-commutative version of the Jackiw-Teitelboim gravity in two dimensions which has a linear potential for the dilaton fields. We study whether it is possible to deform this model by adding quadratic terms to the potential but preserving the number of gauge symmetries. We find that no such deformation exists (provided one does not twist the gauge symmetries). (orig.)
Quantization, geometry and noncommutative structures in mathematics and physics

CERN Document Server

Morales, Pedro; Ocampo, Hernán; Paycha, Sylvie; Lega, Andrés

2017-01-01

This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics. The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics. A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt. The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a non-commutative setup, where Hopf a...
Matrix models as non-commutative field theories on R3

International Nuclear Information System (INIS)

Livine, Etera R

2009-01-01

In the context of spin foam models for quantum gravity, group field theories are a useful tool allowing on the one hand a non-perturbative formulation of the partition function and on the other hand admitting an interpretation as generalized matrix models. Focusing on 2d group field theories, we review their explicit relation to matrix models and show their link to a class of non-commutative field theories invariant under a quantum-deformed 3d Poincare symmetry. This provides a simple relation between matrix models and non-commutative geometry. Moreover, we review the derivation of effective 2d group field theories with non-trivial propagators from Boulatov's group field theory for 3d quantum gravity. Besides the fact that this gives a simple and direct derivation of non-commutative field theories for the matter dynamics coupled to (3d) quantum gravity, these effective field theories can be expressed as multi-matrix models with a non-trivial coupling between matrices of different sizes. It should be interesting to analyze this new class of theories, both from the point of view of matrix models as integrable systems and for the study of non-commutative field theories.
Quantum gravity boundary terms from the spectral action of noncommutative space.

Science.gov (United States)

Chamseddine, Ali H; Connes, Alain

2007-08-17

We study the boundary terms of the spectral action of the noncommutative space, defined by the spectral triple dictated by the physical spectrum of the standard model, unifying gravity with all other fundamental interactions. We prove that the spectral action predicts uniquely the gravitational boundary term required for consistency of quantum gravity with the correct sign and coefficient. This is a remarkable result given the lack of freedom in the spectral action to tune this term.
Group field theory with noncommutative metric variables.

Science.gov (United States)

Baratin, Aristide; Oriti, Daniele

2010-11-26

We introduce a dual formulation of group field theories as a type of noncommutative field theories, making their simplicial geometry manifest. For Ooguri-type models, the Feynman amplitudes are simplicial path integrals for BF theories. We give a new definition of the Barrett-Crane model for gravity by imposing the simplicity constraints directly at the level of the group field theory action.
Self Sustained Traversable Wormholes Induced by Gravity’s Rainbow and Noncommutative Geometry

Directory of Open Access Journals (Sweden)

Garattini Remo

2013-09-01

Full Text Available We compare the effects of Noncommutative Geometry and Gravity’s Rainbow on traversable wormholes which are sustained by their own gravitational quantum fluctuations. Fixing the geometry on a well tested model, we find that the final result shows that the wormhole is of the Planckian size. This means that the traversability of the wormhole is in principle, but not in practice.
Noncommutative spectral geometry, Bogoliubov transformations and neutrino oscillations

International Nuclear Information System (INIS)

Gargiulo, Maria Vittoria; Vitiello, Giuseppe; Sakellariadou, Mairi

2015-01-01

In this report we show that neutrino mixing is intrinsically contained in Connes’ noncommutatives pectral geometry construction, thanks to the introduction of the doubling of algebra, which is connected to the Bogoliubov transformation. It is known indeed that these transformations are responsible for the mixing, turning the mass vacuum state into the flavor vacuum state, in such a way that mass and flavor vacuum states are not unitary equivalent. There is thus a red thread that binds the doubling of algebra of Connes’ model to the neutrino mixing. (paper)
Some homological properties of skew PBW extensions arising in non-commutative algebraic geometry

Directory of Open Access Journals (Sweden)

Lezama Oswaldo

2017-06-01

Full Text Available In this short paper we study for the skew PBW (Poincar-Birkhoff-Witt extensions some homological properties arising in non-commutative algebraic geometry, namely, Auslander-Gorenstein regularity, Cohen-Macaulayness and strongly noetherianity. Skew PBW extensions include a considerable number of non-commutative rings of polynomial type such that classical PBW extensions, quantum polynomial rings, multiplicative analogue of the Weyl algebra, some Sklyanin algebras, operator algebras, diffusion algebras, quadratic algebras in 3 variables, among many others. Parametrization of the point modules of some examples is also presented.
A View on Optimal Transport from Noncommutative Geometry

Directory of Open Access Journals (Sweden)

Francesco D'Andrea

2010-07-01

Full Text Available We discuss the relation between the Wasserstein distance of order 1 between probability distributions on a metric space, arising in the study of Monge-Kantorovich transport problem, and the spectral distance of noncommutative geometry. Starting from a remark of Rieffel on compact manifolds, we first show that on any - i.e. non-necessary compact - complete Riemannian spin manifolds, the two distances coincide. Then, on convex manifolds in the sense of Nash embedding, we provide some natural upper and lower bounds to the distance between any two probability distributions. Specializing to the Euclidean space R^n, we explicitly compute the distance for a particular class of distributions generalizing Gaussian wave packet. Finally we explore the analogy between the spectral and the Wasserstein distances in the noncommutative case, focusing on the standard model and the Moyal plane. In particular we point out that in the two-sheet space of the standard model, an optimal-transport interpretation of the metric requires a cost function that does not vanish on the diagonal. The latest is similar to the cost function occurring in the relativistic heat equation.
Gravity is Geometry.

Science.gov (United States)

MacKeown, P. K.

1984-01-01

Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)
Gravitational amplitudes in black hole evaporation: the effect of non-commutative geometry

International Nuclear Information System (INIS)

Grezia, Elisabetta Di; Esposito, Giampiero; Miele, Gennaro

2006-01-01

Recent work in the literature has studied the quantum-mechanical decay of a Schwarzschild-like black hole, formed by gravitational collapse, into almost-flat spacetime and weak radiation at a very late time. The relevant quantum amplitudes have been evaluated for bosonic and fermionic fields, showing that no information is lost in collapse to a black hole. On the other hand, recent developments in non-commutative geometry have shown that, in general relativity, the effects of non-commutativity can be taken into account by keeping the standard form of the Einstein tensor on the left-hand side of the field equations and introducing a modified energy-momentum tensor as a source on the right-hand side. The present paper, relying on the recently obtained non-commutativity effect on a static, spherically symmetric metric, considers from a new perspective the quantum amplitudes in black hole evaporation. The general relativity analysis of spin-2 amplitudes is shown to be modified by a multiplicative factor F depending on a constant non-commutativity parameter and on the upper limit R of the radial coordinate. Limiting forms of F are derived which are compatible with the adiabatic approximation here exploited. Approximate formulae for the particle emission rate are also obtained within this framework
On Born's deformed reciprocal complex gravitational theory and noncommutative gravity

International Nuclear Information System (INIS)

Castro, Carlos

2008-01-01

Born's reciprocal relativity in flat spacetimes is based on the principle of a maximal speed limit (speed of light) and a maximal proper force (which is also compatible with a maximal and minimal length duality) and where coordinates and momenta are unified on a single footing. We extend Born's theory to the case of curved spacetimes and construct a deformed Born reciprocal general relativity theory in curved spacetimes (without the need to introduce star products) as a local gauge theory of the deformed Quaplectic group that is given by the semi-direct product of U(1,3) with the deformed (noncommutative) Weyl-Heisenberg group corresponding to noncommutative generators [Z a ,Z b ]≠0. The Hermitian metric is complex-valued with symmetric and nonsymmetric components and there are two different complex-valued Hermitian Ricci tensors R μν ,S μν . The deformed Born's reciprocal gravitational action linear in the Ricci scalars R,S with Torsion-squared terms and BF terms is presented. The plausible interpretation of Z μ =E μ a Z a as noncommuting p-brane background complex spacetime coordinates is discussed in the conclusion, where E μ a is the complex vielbein associated with the Hermitian metric G μν =g (μν) +ig [μν] =E μ a E-bar ν b η ab . This could be one of the underlying reasons why string-theory involves gravity
The Gribov problem in noncommutative QED

Energy Technology Data Exchange (ETDEWEB)

Canfora, Fabrizio [Centro de Estudios Científicos (CECS),Casilla 1469, Valdivia (Chile); Kurkov, Maxim A. [Dipartimento di Matematica, Università di Napoli Federico II,Monte S. Angelo, Via Cintia, 80126 Napoli (Italy); CMCC-Universidade Federal do ABC,Santo André, S.P. (Brazil); INFN, Sezione di Napoli,Monte S. Angelo, Via Cintia, 80126 Napoli (Italy); Rosa, Luigi; Vitale, Patrizia [Dipartimento di Fisica, Università di Napoli Federico II,Monte S. Angelo, Via Cintia, 80126 Napoli (Italy); INFN, Sezione di Napoli,Monte S. Angelo, Via Cintia, 80126 Napoli (Italy)

2016-01-04

It is shown that in the noncommutative version of QED (NCQED) Gribov copies induced by the noncommutativity of space-time appear in the Landau gauge. This is a genuine effect of noncommutative geometry which disappears when the noncommutative parameter vanishes.

Emergent gravity and noncommutative branes from Yang-Mills matrix models

International Nuclear Information System (INIS)

Steinacker, Harold

2009-01-01

The framework of emergent gravity arising from Yang-Mills matrix models is developed further, for general noncommutative branes embedded in R D . The effective metric on the brane turns out to have a universal form reminiscent of the open string metric, depending on the dynamical Poisson structure and the embedding metric in R D . A covariant form of the tree-level equations of motion is derived, and the Newtonian limit is discussed. This points to the necessity of branes in higher dimensions. The quantization is discussed qualitatively, which singles out the IKKT model as a prime candidate for a quantum theory of gravity coupled to matter. The Planck scale is then identified with the scale of N=4 SUSY breaking. A mechanism for avoiding the cosmological constant problem is exhibited
Non-commutative geometry on quantum phase-space

International Nuclear Information System (INIS)

Reuter, M.

1995-06-01

A non-commutative analogue of the classical differential forms is constructed on the phase-space of an arbitrary quantum system. The non-commutative forms are universal and are related to the quantum mechanical dynamics in the same way as the classical forms are related to classical dynamics. They are constructed by applying the Weyl-Wigner symbol map to the differential envelope of the linear operators on the quantum mechanical Hilbert space. This leads to a representation of the non-commutative forms considered by A. Connes in terms of multiscalar functions on the classical phase-space. In an appropriate coincidence limit they define a quantum deformation of the classical tensor fields and both commutative and non-commutative forms can be studied in a unified framework. We interprete the quantum differential forms in physical terms and comment on possible applications. (orig.)
Scalar curvature in conformal geometry of Connes-Landi noncommutative manifolds

Science.gov (United States)

Liu, Yang

2017-11-01

We first propose a conformal geometry for Connes-Landi noncommutative manifolds and study the associated scalar curvature. The new scalar curvature contains its Riemannian counterpart as the commutative limit. Similar to the results on noncommutative two tori, the quantum part of the curvature consists of actions of the modular derivation through two local curvature functions. Explicit expressions for those functions are obtained for all even dimensions (greater than two). In dimension four, the one variable function shows striking similarity to the analytic functions of the characteristic classes appeared in the Atiyah-Singer local index formula, namely, it is roughly a product of the j-function (which defines the A ˆ -class of a manifold) and an exponential function (which defines the Chern character of a bundle). By performing two different computations for the variation of the Einstein-Hilbert action, we obtain deep internal relations between two local curvature functions. Straightforward verification for those relations gives a strong conceptual confirmation for the whole computational machinery we have developed so far, especially the Mathematica code hidden behind the paper.
Towards Noncommutative Topological Quantum Field Theory: New invariants for 3-manifolds

International Nuclear Information System (INIS)

Zois, I.P.

2016-01-01

We present some ideas for a possible Noncommutative Topological Quantum Field Theory (NCTQFT for short) and Noncommutative Floer Homology (NCFH for short). Our motivation is two-fold and it comes both from physics and mathematics: On the one hand we argue that NCTQFT is the correct mathematical framework for a quantum field theory of all known interactions in nature (including gravity). On the other hand we hope that a possible NCFH will apply to practically every 3-manifold (and not only to homology 3-spheres as ordinary Floer Homology currently does). The two motivations are closely related since, at least in the commutative case, Floer Homology Groups constitute the space of quantum observables of (3+1)-dim Topological Quantum Field Theory. Towards this goal we define some new invariants for 3-manifolds using the space of taut codim-1 foliations modulo coarse isotopy along with various techniques from noncommutative geometry. (paper)
Quantum group of isometries in classical and noncommutative geometry

International Nuclear Information System (INIS)

Goswami, D.

2007-04-01

We formulate a quantum generalization of the notion of the group of Riemannian isometries for a compact Riemannian manifold, by introducing a natural notion of smooth and isometric action by a compact quantum group on a classical or noncommutative manifold described by spectral triples, and then proving the existence of a universal object (called the quantum isometry group) in the category of compact quantum groups acting smoothly and isometrically on a given (possibly noncommutative) manifold. Our formulation accommodates spectral triples which are not of type II. We give an explicit description of quantum isometry groups of commutative and noncommutative tori, and in this context, obtain the quantum double torus defined in [7] as the universal quantum group of holomorphic isometries of the noncommutative torus. (author)
Noncommutative geometry and fluid dynamics

International Nuclear Information System (INIS)

Das, Praloy; Ghosh, Subir

2016-01-01

In the present paper we have developed a Non-Commutative (NC) generalization of perfect fluid model from first principles, in a Hamiltonian framework. The noncommutativity is introduced at the Lagrangian (particle) coordinate space brackets and the induced NC fluid bracket algebra for the Eulerian (fluid) field variables is derived. Together with a Hamiltonian this NC algebra generates the generalized fluid dynamics that satisfies exact local conservation laws for mass and energy, thereby maintaining mass and energy conservation. However, nontrivial NC correction terms appear in the charge and energy fluxes. Other non-relativistic spacetime symmetries of the NC fluid are also discussed in detail. This constitutes the study of kinematics and dynamics of NC fluid. In the second part we construct an extension of the Friedmann-Robertson-Walker (FRW) cosmological model based on the NC fluid dynamics presented here. We outline the way in which NC effects generate cosmological perturbations bringing about anisotropy and inhomogeneity in the model. We also derive a NC extended Friedmann equation. (orig.)
Noncommutative geometry and fluid dynamics

Energy Technology Data Exchange (ETDEWEB)

Das, Praloy; Ghosh, Subir [Indian Statistical Institute, Physics and Applied Mathematics Unit, Kolkata (India)

2016-11-15

In the present paper we have developed a Non-Commutative (NC) generalization of perfect fluid model from first principles, in a Hamiltonian framework. The noncommutativity is introduced at the Lagrangian (particle) coordinate space brackets and the induced NC fluid bracket algebra for the Eulerian (fluid) field variables is derived. Together with a Hamiltonian this NC algebra generates the generalized fluid dynamics that satisfies exact local conservation laws for mass and energy, thereby maintaining mass and energy conservation. However, nontrivial NC correction terms appear in the charge and energy fluxes. Other non-relativistic spacetime symmetries of the NC fluid are also discussed in detail. This constitutes the study of kinematics and dynamics of NC fluid. In the second part we construct an extension of the Friedmann-Robertson-Walker (FRW) cosmological model based on the NC fluid dynamics presented here. We outline the way in which NC effects generate cosmological perturbations bringing about anisotropy and inhomogeneity in the model. We also derive a NC extended Friedmann equation. (orig.)
From quantum gravity to quantum field theory via noncommutative geometry

International Nuclear Information System (INIS)

Aastrup, Johannes; Grimstrup, Jesper Møller

2014-01-01

A link between canonical quantum gravity and fermionic quantum field theory is established in this paper. From a spectral triple construction, which encodes the kinematics of quantum gravity, we construct semi-classical states which, in a semi-classical limit, give a system of interacting fermions in an ambient gravitational field. The emergent interaction involves flux tubes of the gravitational field. In the additional limit, where all gravitational degrees of freedom are turned off, a free fermionic quantum field theory emerges. (paper)
Vacuum energy from noncommutative models

Science.gov (United States)

Mignemi, S.; Samsarov, A.

2018-04-01

The vacuum energy is computed for a scalar field in a noncommutative background in several models of noncommutative geometry. One may expect that the noncommutativity introduces a natural cutoff on the ultraviolet divergences of field theory. Our calculations show however that this depends on the particular model considered: in some cases the divergences are suppressed and the vacuum energy is only logarithmically divergent, in other cases they are stronger than in the commutative theory.
Accretion onto a noncommutative geometry inspired black hole

Energy Technology Data Exchange (ETDEWEB)

Kumar, Rahul [Jamia Millia Islamia, Centre for Theoretical Physics, New Delhi (India); Ghosh, Sushant G. [Jamia Millia Islamia, Centre for Theoretical Physics, New Delhi (India); Jamia Millia Islamia, Multidisciplinary Centre for Advanced Research and Studies (MCARS), New Delhi (India); University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban (South Africa)

2017-09-15

The spherically symmetric accretion onto a noncommutative (NC) inspired Schwarzschild black hole is treated for a polytropic fluid. The critical accretion rate M, sonic speed a{sub s} and other flow parameters are generalized for the NC inspired static black hole and compared with the results obtained for the standard Schwarzschild black holes. Also explicit expressions for gas compression ratios and temperature profiles below the accretion radius and at the event horizon are derived. This analysis is a generalization of Michel's solution to the NC geometry. Owing to the NC corrected black hole, the accretion flow parameters also have been modified. It turns out that M ∼ M{sup 2} is still achievable but r{sub s} seems to be substantially decreased due to the NC effects. They in turn do affect the accretion process. (orig.)
Stability analysis of lower dimensional gravastars in noncommutative geometry

Energy Technology Data Exchange (ETDEWEB)

Banerjee, Ayan [Jadavpur University, Department of Mathematics, Kolkata (India); Hansraj, Sudan [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban (South Africa)

2016-11-15

The Banados et al. (Phys. Rev. Lett 69:1849, 1992), black hole solution is revamped from the Einstein field equations in (2 + 1)-dimensional anti-de Sitter spacetime, in a context of noncommutative geometry (Phys. Rev. D 87:084014, 2013). In this article, we explore the exact gravastar solutions in three-dimensional anti-de Sitter space given in the same geometry. As a first step we derive BTZ solution assuming the source of energy density as point-like structures in favor of smeared objects, where the particle mass M, is diffused throughout a region of linear size √(α) and is described by a Gaussian function of finite width rather than a Dirac delta function. We matched our interior solution to an exterior BTZ spacetime at a junction interface situated outside the event horizon. Furthermore, a stability analysis is carried out for the specific case when χ < 0.214 under radial perturbations about the static equilibrium solutions. To give theoretical support we are also trying to explore their physical properties and characteristics. (orig.)
A short essay on quantum black holes and underlying noncommutative quantized space-time

International Nuclear Information System (INIS)

Tanaka, Sho

2017-01-01

We emphasize the importance of noncommutative geometry or Lorenz-covariant quantized space-time towards the ultimate theory of quantum gravity and Planck scale physics. We focus our attention on the statistical and substantial understanding of the Bekenstein–Hawking area-entropy law of black holes in terms of the kinematical holographic relation (KHR). KHR manifestly holds in Yang’s quantized space-time as the result of kinematical reduction of spatial degrees of freedom caused by its own nature of noncommutative geometry, and plays an important role in our approach without any recourse to the familiar hypothesis, so-called holographic principle. In the present paper, we find a unified form of KHR applicable to the whole region ranging from macroscopic to microscopic scales in spatial dimension d = 3. We notice a possibility of nontrivial modification of area-entropy law of black holes which becomes most remarkable in the extremely microscopic system close to Planck scale. (paper)
Instantons, quivers and noncommutative Donaldson-Thomas theory

Science.gov (United States)

Cirafici, Michele; Sinkovics, Annamaria; Szabo, Richard J.

2011-12-01

We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analyzing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge theory localizes on noncommutative instantons which can be classified in terms of three-dimensional Young diagrams with a colouring of boxes according to the orbifold group. We construct a moduli space for these gauge field configurations which allows us to compute its virtual numbers via the counting of representations of a quiver with relations. The quiver encodes the instanton dynamics of the noncommutative gauge theory, and is associated to the geometry of the singularity via the generalized McKay correspondence. The index of BPS states which compute the noncommutative Donaldson-Thomas invariants is realized via topological quantum mechanics based on the quiver data. We illustrate these constructions with several explicit examples, involving also higher rank Coulomb branch invariants and geometries with compact divisors, and connect our approach with other ones in the literature.
Instantons, quivers and noncommutative Donaldson-Thomas theory

Energy Technology Data Exchange (ETDEWEB)

Cirafici, Michele, E-mail: cirafici@math.ist.utl.pt [Centro de Analise Matematica, Geometria e Sistemas Dinamicos, Departamento de Matematica, Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001 Lisboa (Portugal); Sinkovics, Annamaria, E-mail: A.Sinkovics@damtp.cam.ac.uk [Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Szabo, Richard J., E-mail: R.J.Szabo@ma.hw.ac.uk [Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS (United Kingdom); Maxwell Institute for Mathematical Sciences, Edinburgh (United Kingdom)

2011-12-11

We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analyzing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge theory localizes on noncommutative instantons which can be classified in terms of three-dimensional Young diagrams with a colouring of boxes according to the orbifold group. We construct a moduli space for these gauge field configurations which allows us to compute its virtual numbers via the counting of representations of a quiver with relations. The quiver encodes the instanton dynamics of the noncommutative gauge theory, and is associated to the geometry of the singularity via the generalized McKay correspondence. The index of BPS states which compute the noncommutative Donaldson-Thomas invariants is realized via topological quantum mechanics based on the quiver data. We illustrate these constructions with several explicit examples, involving also higher rank Coulomb branch invariants and geometries with compact divisors, and connect our approach with other ones in the literature.
Weinberg-Salam theory in non-commutative geometry

International Nuclear Information System (INIS)

Morita, Katsusada; Okumura, Yoshitaka.

1994-01-01

Ordinary differential calculus on smooth manifold is generalized so as to construct gauge theory coupled to fermions on discrete space M 4 xZ 2 which is an underlying space-time in the non-commutative geometry for the standard model. We can reproduce not only the bosonic sector but also the fermionic sector of the Weinberg-Salam theory without recourse to the Dirac operator at the outset. Treatment of the fermionic sector is based on the generalized spinor one-forms from which the Dirac lagrangian is derived through taking the inner product. Two model constructions are presented using our formalism, both giving the classical mass relation m H = √2m w . The first model leaves the Weinberg angle arbitrary as usual, while the second one predicts sin 2 θ w = 1/4 in the tree level. This prediction is the same as that of Connes but we obtain it from correct hypercharge assignment of 2x2 matrix-valued Higgs field and from vanishing photon mass, thereby dispensing with Connes' 0-trace condition or the equivalent. (author)
Probing noncommutative theories with quantum optical experiments

Directory of Open Access Journals (Sweden)

Sanjib Dey

2017-11-01

Full Text Available One of the major difficulties of modern science underlies at the unification of general relativity and quantum mechanics. Different approaches towards such theory have been proposed. Noncommutative theories serve as the root of almost all such approaches. However, the identification of the appropriate passage to quantum gravity is suffering from the inadequacy of experimental techniques. It is beyond our ability to test the effects of quantum gravity thorough the available scattering experiments, as it is unattainable to probe such high energy scale at which the effects of quantum gravity appear. Here we propose an elegant alternative scheme to test such theories by detecting the deformations emerging from the noncommutative structures. Our protocol relies on the novelty of an opto-mechanical experimental setup where the information of the noncommutative oscillator is exchanged via the interaction with an optical pulse inside an optical cavity. We also demonstrate that our proposal is within the reach of current technology and, thus, it could uncover a feasible route towards the realization of quantum gravitational phenomena thorough a simple table-top experiment.
Kerr geometry in f(T) gravity

Energy Technology Data Exchange (ETDEWEB)

Bejarano, Cecilia; Guzman, Maria Jose [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Ferraro, Rafael [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Universidad de Buenos Aires, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina)

2015-02-01

Null tetrads are shown to be a valuable tool in teleparallel theories of modified gravity. We use them to prove that Kerr geometry remains a solution for a wide family of f(T) theories of gravity. (orig.)
Kerr geometry in f(T) gravity

International Nuclear Information System (INIS)

Bejarano, Cecilia; Guzman, Maria Jose; Ferraro, Rafael

2015-01-01

Null tetrads are shown to be a valuable tool in teleparallel theories of modified gravity. We use them to prove that Kerr geometry remains a solution for a wide family of f(T) theories of gravity. (orig.)
((F, D1), D3) bound state, S-duality and noncommutative open string/Yang-Mills theory

International Nuclear Information System (INIS)

Lu, J.X.; Roy, S.; Singh, H.

2000-01-01

We study decoupling limits and S-dualities for noncommutative open string/Yang-Mills theory in a gravity setup by considering an SL(2,Z) invariant supergravity solution of the form ((F, D1), D3) bound state of type IIB string theory. This configuration can be regarded as D3-branes with both electric and magnetic fields turned on along one of the spatial directions of the brane and preserves half of the space-time supersymmetries of the string theory. Our study indicates that there exists a decoupling limit for which the resulting theory is an open string theory defined in a geometry with noncommutativity in both space-time and space-space directions. We study S-duality of this noncommutative open string (NCOS) and find that the same decoupling limit in the S-dual description gives rise to a space-space noncommutative Yang-Mills theory (NCYM). We also discuss independently the decoupling limit for NCYM in this D3 brane background. Here we find that S-duality of NCYM theory does not always give a NCOS theory. Instead, it can give an ordinary Yang-Mills with a singular metric and an infinitely large coupling. We also find that the open string coupling relation between the two S-duality related theories is modified such that S-duality of a strongly coupled open-string/Yang-Mills theory does not necessarily give a weakly coupled theory. The relevant gravity dual descriptions of NCOS/NCYM are also given. (author)
Mapping spaces and automorphism groups of toric noncommutative spaces

Science.gov (United States)

Barnes, Gwendolyn E.; Schenkel, Alexander; Szabo, Richard J.

2017-09-01

We develop a sheaf theory approach to toric noncommutative geometry which allows us to formalize the concept of mapping spaces between two toric noncommutative spaces. As an application, we study the `internalized' automorphism group of a toric noncommutative space and show that its Lie algebra has an elementary description in terms of braided derivations.

Optimization of polynomials in non-commuting variables

CERN Document Server

Burgdorf, Sabine; Povh, Janez

2016-01-01

This book presents recent results on positivity and optimization of polynomials in non-commuting variables. Researchers in non-commutative algebraic geometry, control theory, system engineering, optimization, quantum physics and information science will find the unified notation and mixture of algebraic geometry and mathematical programming useful. Theoretical results are matched with algorithmic considerations; several examples and information on how to use NCSOStools open source package to obtain the results provided. Results are presented on detecting the eigenvalue and trace positivity of polynomials in non-commuting variables using Newton chip method and Newton cyclic chip method, relaxations for constrained and unconstrained optimization problems, semidefinite programming formulations of the relaxations and finite convergence of the hierarchies of these relaxations, and the practical efficiency of algorithms.
Discreteness of area in noncommutative space

Energy Technology Data Exchange (ETDEWEB)

Amelino-Camelia, Giovanni [Dipartimento di Fisica, Universita di Roma ' La Sapienza' and Sez. Roma1 INFN, P.le A. Moro 2, 00185 Roma (Italy)], E-mail: amelino@roma1.infn.it; Gubitosi, Giulia; Mercati, Flavio [Dipartimento di Fisica, Universita di Roma ' La Sapienza' and Sez. Roma1 INFN, P.le A. Moro 2, 00185 Roma (Italy)

2009-06-08

We introduce an area operator for the Moyal noncommutative plane. We find that the spectrum is discrete, but, contrary to the expectation formulated by other authors, not characterized by a 'minimum-area principle'. We show that an intuitive analysis of the uncertainty relations obtained from Moyal-plane noncommutativity is fully consistent with our results for the spectrum, and we argue that our area operator should be generalizable to several other noncommutative spaces. We also observe that the properties of distances and areas in the Moyal plane expose some weaknesses in the line of reasoning adopted in some of the heuristic analyses of the measurability of geometric spacetime observables in the quantum-gravity realm.
Discreteness of area in noncommutative space

International Nuclear Information System (INIS)

Amelino-Camelia, Giovanni; Gubitosi, Giulia; Mercati, Flavio

2009-01-01

We introduce an area operator for the Moyal noncommutative plane. We find that the spectrum is discrete, but, contrary to the expectation formulated by other authors, not characterized by a 'minimum-area principle'. We show that an intuitive analysis of the uncertainty relations obtained from Moyal-plane noncommutativity is fully consistent with our results for the spectrum, and we argue that our area operator should be generalizable to several other noncommutative spaces. We also observe that the properties of distances and areas in the Moyal plane expose some weaknesses in the line of reasoning adopted in some of the heuristic analyses of the measurability of geometric spacetime observables in the quantum-gravity realm.
Structural aspects of quantum field theory and noncommutative geometry

CERN Document Server

Grensing, Gerhard

2013-01-01

This book is devoted to the subject of quantum field theory. It is divided into two volumes. The first can serve as a textbook on the main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation. The first volume is directed at graduate students who want to learn the basic facts about quantum field theory. It begins with a gentle introduction to classical field theory, including the standard model of particle physics, general relativity, and also supergravity. The transition to quantized fields is performed with path integral techniques, by means of which the one-loop renormalization of a self-interacting scalar quantum field, of quantum electrodynamics, and the asymptotic freedom of quantum chromodynamics is treated. In the last part of the first volume, the application of path integral methods to systems of quantum statistical mechanics is covered. The book ends with a r...
Vectors and covectors in non-commutative setting

OpenAIRE

Parfionov, G. N.; Romashev, Yu. A.; Zapatrine, R. R.

1995-01-01

Following the guidelines of classical differential geometry the `building material' for the tensor calculus in non-commutative geometry is suggested. The algebraic account of moduli of vectors and covectors is carried out.
Hořava-Lifshitz gravity from dynamical Newton-Cartan geometry

International Nuclear Information System (INIS)

Hartong, Jelle; Obers, Niels A.

2015-01-01

Recently it has been established that torsional Newton-Cartan (TNC) geometry is the appropriate geometrical framework to which non-relativistic field theories couple. We show that when these geometries are made dynamical they give rise to Hořava-Lifshitz (HL) gravity. Projectable HL gravity corresponds to dynamical Newton-Cartan (NC) geometry without torsion and non-projectable HL gravity corresponds to dynamical NC geometry with twistless torsion (hypersurface orthogonal foliation). We build a precise dictionary relating all fields (including the scalar khronon), their transformations and other properties in both HL gravity and dynamical TNC geometry. We use TNC invariance to construct the effective action for dynamical twistless torsional Newton-Cartan geometries in 2+1 dimensions for dynamical exponent 1geometries. We argue that TNC geometry, which is manifestly diffeomorphism covariant, is a natural geometrical framework underlying HL gravity and discuss some of its implications.
Hořava-Lifshitz gravity from dynamical Newton-Cartan geometry

Energy Technology Data Exchange (ETDEWEB)

Hartong, Jelle [Physique Théorique et Mathématique and International Solvay Institutes, Université Libre de Bruxelles,C.P. 231, 1050 Brussels (Belgium); Obers, Niels A. [The Niels Bohr Institute, Copenhagen University,Blegdamsvej 17, DK-2100 Copenhagen Ø (Denmark)

2015-07-29

Recently it has been established that torsional Newton-Cartan (TNC) geometry is the appropriate geometrical framework to which non-relativistic field theories couple. We show that when these geometries are made dynamical they give rise to Hořava-Lifshitz (HL) gravity. Projectable HL gravity corresponds to dynamical Newton-Cartan (NC) geometry without torsion and non-projectable HL gravity corresponds to dynamical NC geometry with twistless torsion (hypersurface orthogonal foliation). We build a precise dictionary relating all fields (including the scalar khronon), their transformations and other properties in both HL gravity and dynamical TNC geometry. We use TNC invariance to construct the effective action for dynamical twistless torsional Newton-Cartan geometries in 2+1 dimensions for dynamical exponent 1geometries. We argue that TNC geometry, which is manifestly diffeomorphism covariant, is a natural geometrical framework underlying HL gravity and discuss some of its implications.
Noncommutative generalization of SU(n)-principal fiber bundles: a review

International Nuclear Information System (INIS)

Masson, T

2008-01-01

This is an extended version of a communication made at the international conference 'Noncommutative Geometry and Physics' held at Orsay in april 2007. In this proceeding, we make a review of some noncommutative constructions connected to the ordinary fiber bundle theory. The noncommutative algebra is the endomorphism algebra of a SU(n)-vector bundle, and its differential calculus is based on its Lie algebra of derivations. It is shown that this noncommutative geometry contains some of the most important constructions introduced and used in the theory of connections on vector bundles, in particular, what is needed to introduce gauge models in physics, and it also contains naturally the essential aspects of the Higgs fields and its associated mechanics of mass generation. It permits one also to extend some previous constructions, as for instance symmetric reduction of (here noncommutative) connections. From a mathematical point of view, these geometrico-algebraic considerations highlight some new point on view, in particular we introduce a new construction of the Chern characteristic classes
Note on the extended noncommutativity of coordinates

International Nuclear Information System (INIS)

Boulahoual, Amina; Sedra, My. Brahim

2001-04-01

We present in this short note an idea about a possible extension of the standard noncommutative algebra to the formal differential operators framework. In this sense, we develop an analysis and derive an extended noncommutative algebra given by [x a , x b ] * =i(θ+χ) ab where θ ab , is the standard noncommutative parameter and χ ab (x)≡χ ab μ (x)δ μ =1/2(x a θ μ b -x b θ a )δ μ is an antisymmetric non-constant vector-field shown to play the role of the extended deformation parameter. This idea was motivated by the importance of noncommutative geometry framework in the current subject of D-brane and matrix theory physics. (author)
Noncommutative Black Holes at the LHC

Science.gov (United States)

Villhauer, Elena Michelle

2017-12-01

Based on the latest public results, 13 TeV data from the Large Hadron Collider at CERN has not indicated any evidence of hitherto tested models of quantum black holes, semiclassical black holes, or string balls. Such models have predicted signatures of particles with high transverse momenta. Noncommutative black holes remain an untested model of TeV-scale gravity that offers the starkly different signature of particles with relatively low transverse momenta. Considerations for a search for charged noncommutative black holes using the ATLAS detector will be discussed.
Vector fields and differential operators: noncommutative case

International Nuclear Information System (INIS)

Borowiec, A.

1997-01-01

A notion of Cartan pairs as an analogy of vector fields in the realm of noncommutative geometry has been proposed previously. In this paper an outline is given of the construction of a noncommutative analogy of the algebra of differential operators as well as its (algebraic) Fock space realization. Co-universal vector fields and covariant derivatives will also be discussed
Noncommutative induced gauge theories on Moyal spaces

International Nuclear Information System (INIS)

Wallet, J-C

2008-01-01

Noncommutative field theories on Moyal spaces can be conveniently handled within a framework of noncommutative geometry. Several renormalisable matter field theories that are now identified are briefly reviewed. The construction of renormalisable gauge theories on these noncommutative Moyal spaces, which remains so far a challenging problem, is then closely examined. The computation in 4-D of the one-loop effective gauge theory generated from the integration over a scalar field appearing in a renormalisable theory minimally coupled to an external gauge potential is presented. The gauge invariant effective action is found to involve, beyond the expected noncommutative version of the pure Yang-Mills action, additional terms that may be interpreted as the gauge theory counterpart of the harmonic term, which for the noncommutative ψ 4 -theory on Moyal space ensures renormalisability. A class of possible candidates for renormalisable gauge theory actions defined on Moyal space is presented and discussed
Stabilization of compactification volume in a noncommutative mini-super-phase-space

International Nuclear Information System (INIS)

Khosravi, N.; Sepangi, H.R.; Sheikh-Jabbari, M.M.

2007-01-01

We consider a class of generalized FRW type metrics in the context of higher dimensional Einstein gravity in which the extra dimensions are allowed to have different scale factors. It is shown that noncommutativity between the momenta conjugate to the internal space scale factors controls the power-law behavior of the scale factors in the extra dimensions, taming it to an oscillatory behavior. Hence noncommutativity among the internal momenta of the mini-super-phase-space can be used to explain stabilization of the compactification volume of the internal space in a higher dimensional gravity theory
Accretion onto a noncommutative-inspired Schwarzschild black hole

Science.gov (United States)

Gangopadhyay, Sunandan; Paik, Biplab; Mandal, Rituparna

2018-05-01

In this paper, we investigate the problem of ordinary baryonic matter accretion onto the noncommutative (NC) geometry-inspired Schwarzschild black hole. The fundamental equations governing the spherically symmetric steady state matter accretion are deduced. These equations are seen to be modified due to the presence of noncommutativity. The matter accretion rate is computed and is found to increase rapidly with the increase in strength of the NC parameter. The sonic radius reduces while the sound speed at the sonic point increases with the increase in the strength of noncommutativity. The profile of the thermal environment is finally investigated below the sonic radius and at the event horizon and is found to be affected by noncommutativity.
On Spectral Triples in Quantum Gravity I

DEFF Research Database (Denmark)

Aastrup, Johannes; M. Grimstrup, Jesper; Nest, Ryszard

2009-01-01

This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator which resembles a global functional derivation operator....... The interaction between the Dirac operator and the algebra reproduces the Poisson structure of General Relativity. Moreover, the associated Hilbert space corresponds, up to a discrete symmetry group, to the Hilbert space of diffeomorphism invariant states known from Loop Quantum Gravity. Correspondingly......, the square of the Dirac operator has, in terms of canonical quantum gravity, the form of a global area-squared operator. Furthermore, the spectral action resembles a partition function of Quantum Gravity. The construction is background independent and is based on an inductive system of triangulations...
The theory of pseudo-differential operators on the noncommutative n-torus

Science.gov (United States)

Tao, J.

2018-02-01

The methods of spectral geometry are useful for investigating the metric aspects of noncommutative geometry and in these contexts require extensive use of pseudo-differential operators. In a foundational paper, Connes showed that, by direct analogy with the theory of pseudo-differential operators on finite-dimensional real vector spaces, one may derive a similar pseudo-differential calculus on noncommutative n-tori, and with the development of this calculus came many results concerning the local differential geometry of noncommutative tori for n=2,4, as shown in the groundbreaking paper in which the Gauss-Bonnet theorem on the noncommutative two-torus is proved and later papers. Certain details of the proofs in the original derivation of the calculus were omitted, such as the evaluation of oscillatory integrals, so we make it the objective of this paper to fill in all the details. After reproving in more detail the formula for the symbol of the adjoint of a pseudo-differential operator and the formula for the symbol of a product of two pseudo-differential operators, we extend these results to finitely generated projective right modules over the noncommutative n-torus. Then we define the corresponding analog of Sobolev spaces and prove equivalents of the Sobolev and Rellich lemmas.
Semiclassical quantum gravity: statistics of combinatorial Riemannian geometries

International Nuclear Information System (INIS)

Bombelli, L.; Corichi, A.; Winkler, O.

2005-01-01

This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at ''quantum scales'' and continuum, classical geometries at large scales. Such a correspondence can be meaningfully established when one has a ''semiclassical'' state in the underlying quantum gravity theory, and the uncertainties in the correspondence arise both from quantum fluctuations in this state and from the kinematical procedure of matching a smooth geometry to a discrete one. We focus on the latter type of uncertainty, and suggest the use of statistical geometry as a way to quantify it. With a cell complex as an example of discrete structure, we discuss how to construct quantities that define a smooth geometry, and how to estimate the associated uncertainties. We also comment briefly on how to combine our results with uncertainties in the underlying quantum state, and on their use when considering phenomenological aspects of quantum gravity. (Abstract Copyright [2005], Wiley Periodicals, Inc.)
Noncommutative conformally coupled scalar field cosmology and its commutative counterpart

International Nuclear Information System (INIS)

Barbosa, G.D.

2005-01-01

We study the implications of a noncommutative geometry of the minisuperspace variables for the Friedmann-Robertson-Walker universe with a conformally coupled scalar field. The investigation is carried out by means of a comparative study of the universe evolution in four different scenarios: classical commutative, classical noncommutative, quantum commutative, and quantum noncommutative, the last two employing the Bohmian formalism of quantum trajectories. The role of noncommutativity is discussed by drawing a parallel between its realizations in two possible frameworks for physical interpretation: the NC frame, where it is manifest in the universe degrees of freedom, and in the C frame, where it is manifest through θ-dependent terms in the Hamiltonian. As a result of our comparative analysis, we find that noncommutative geometry can remove singularities in the classical context for sufficiently large values of θ. Moreover, under special conditions, the classical noncommutative model can admit bouncing solutions characteristic of the commutative quantum Friedmann-Robertson-Walker universe. In the quantum context, we find nonsingular universe solutions containing bounces or being periodic in the quantum commutative model. When noncommutativity effects are turned on in the quantum scenario, they can introduce significant modifications that change the singular behavior of the universe solutions or that render them dynamical whenever they are static in the commutative case. The effects of noncommutativity are completely specified only when one of the frames for its realization is adopted as the physical one. Nonsingular solutions in the NC frame can be mapped into singular ones in the C frame
Non-commutative analysis

CERN Document Server

Jorgensen, Palle

2017-01-01

The book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret 'non-commutative analysis' broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.)A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras.The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.
C*-algebras of holonomy-diffeomorphisms and quantum gravity: I

International Nuclear Information System (INIS)

Aastrup, Johannes; Grimstrup, Jesper Møller

2013-01-01

A new approach to a unified theory of quantum gravity based on noncommutative geometry and canonical quantum gravity is presented. The approach is built around a *-algebra generated by local holonomy-diffeomorphisms on a 3-manifold and a quantized Dirac-type operator, the two capturing the kinematics of quantum gravity formulated in terms of Ashtekar variables. We prove that the separable part of the spectrum of the algebra is contained in the space of measurable connections modulo gauge transformations and we give limitations to the non-separable part. The construction of the Dirac-type operator—and thus the application of noncommutative geometry—is motivated by the requirement of diffeomorphism invariance. We conjecture that a semi-finite spectral triple, which is invariant under volume-preserving diffeomorphisms, arises from a GNS construction of a semi-classical state. Key elements of quantum field theory emerge from the construction in a semi-classical limit, as does an almost commutative algebra. Finally, we note that the spectrum of loop quantum gravity emerges from a discretization of our construction. Certain convergence issues are left unresolved. This paper is the first of two where the second paper [1] is concerned with mathematical details and proofs concerning the spectrum of the holonomy-diffeomorphism algebra. (paper)

Algebra, Geometry and Mathematical Physics Conference

CERN Document Server

Paal, Eugen; Silvestrov, Sergei; Stolin, Alexander

2014-01-01

This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and applications; non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization, and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book benefits a broad audience of researchers a...
Lorentz invariant noncommutative algebra for cosmological models coupled to a perfect fluid

International Nuclear Information System (INIS)

Abreu, Everton M.C.; Marcial, Mateus V.; Mendes, Albert C.R.; Oliveira, Wilson

2013-01-01

Full text: In current theoretical physics there is a relevant number of theoretical investigations that lead to believe that at the first moments of our Universe, the geometry was not commutative and the dominating physics at that time was ruled by the laws of noncommutative (NC) geometry. Therefore, the idea is that the physics of the early moments can be constructed based on these concepts. The first published work using the idea of a NC spacetime were carried out by Snyder who believed that NC principles could make the quantum field theory infinities disappear. However, it did not occur and Snyder's ideas were put to sleep for a long time. The main modern motivations that rekindle the investigation about NC field theories came from string theory and quantum gravity. In the context of quantum mechanics for example, R. Banerjee discussed how NC structures appear in planar quantum mechanics providing a useful way for obtaining them. The analysis was based on the NC algebra used in planar quantum mechanics that was originated from 't Hooft's analysis on dissipation and quantization. In this work we carry out a NC algebra analysis of the Friedmann-Robert-Walker model, coupled to a perfect fluid and in the presence of a cosmological constant. The classical field equations are modified, by the introduction of a shift operator, in order to introduce noncommutativity in these models. (author)
Slab Geometry and Segmentation on Seismogenic Subduction Zone; Insight from gravity gradients

Science.gov (United States)

Saraswati, A. T.; Mazzotti, S.; Cattin, R.; Cadio, C.

2017-12-01

Slab geometry is a key parameter to improve seismic hazard assessment in subduction zones. In many cases, information about structures beneath subduction are obtained from geophysical dedicated studies, including geodetic and seismic measurements. However, due to the lack of global information, both geometry and segmentation in seismogenic zone of many subductions remain badly-constrained. Here we propose an alternative approach based on satellite gravity observations. The GOCE (Gravity field and steady-state Ocean Circulation Explorer) mission enables to probe Earth deep mass structures from gravity gradients, which are more sensitive to spatial structure geometry and directional properties than classical gravitational data. Gravity gradients forward modeling of modeled slab is performed by using horizontal and vertical gravity gradient components to better determine slab geophysical model rather than vertical gradient only. Using polyhedron method, topography correction on gravity gradient signal is undertaken to enhance the anomaly signal of lithospheric structures. Afterward, we compare residual gravity gradients with the calculated signals associated with slab geometry. In this preliminary study, straightforward models are used to better understand the characteristic of gravity gradient signals due to deep mass sources. We pay a special attention to the delineation of slab borders and dip angle variations.
Gravity and the structure of noncommutative algebras

International Nuclear Information System (INIS)

Buric, Maja; Madore, John; Grammatikopoulos, Theodoros; Zoupanos, George

2006-01-01

A gravitational field can be defined in terms of a moving frame, which when made noncommutative yields a preferred basis for a differential calculus. It is conjectured that to a linear perturbation of the commutation relations which define the algebra there corresponds a linear perturbation of the gravitational field. This is shown to be true in the case of a perturbation of Minkowski space-time
Noncommutative geometry-inspired rotating black hole in three ...

Indian Academy of Sciences (India)

We ﬁnd a new rotating black hole in three-dimensional anti-de Sitter space using an anisotropic perfect ﬂuid inspired by the noncommutative black hole. We deduce the thermodynamical quantities of this black hole and compare them with those of a rotating BTZ solution and give corrections to the area law to get the exact ...
Kerr geometry in f(T) gravity

OpenAIRE

Bejarano, Cecilia; Ferraro, Rafael; Guzmán, María José

2014-01-01

Null tetrads are shown to be a valuable tool in teleparallel theories of modified gravity. We use them to prove that Kerr geometry remains a solution for a wide family of theories of gravity. Fil: Bejarano, Cecilia Soledad. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Fí...
Open Wilson lines and generalized star product in noncommutative scalar field theories

International Nuclear Information System (INIS)

Kiem, Youngjai; Sato, Haru-Tada; Rey, Soo-Jong; Yee, Jung-Tay

2002-01-01

Open Wilson line operators and a generalized star product have been studied extensively in noncommutative gauge theories. We show that they also show up in noncommutative scalar field theories as universal structures. We first point out that the dipole picture of noncommutative geometry provides an intuitive argument for the robustness of the open Wilson lines and generalized star products therein. We calculate the one-loop effective action of noncommutative scalar field theory with a cubic self-interaction and show explicitly that the generalized star products arise in the nonplanar part. It is shown that, at the low-energy, large noncommutativity limit, the nonplanar part is expressible solely in terms of the scalar open Wilson line operator and descendants
On the Newtonian limit of emergent NC gravity and long-distance corrections

International Nuclear Information System (INIS)

Steinacker, Harold

2009-01-01

We show how Newtonian gravity emerges on 4-dimensional non-commutative spacetime branes in Yang-Mills matrix models. Large matter clusters such as galaxies are embedded in large-scale harmonic deformations of the space-time brane, which screen gravity for long distances. On shorter scales, the local matter distribution reproduces Newtonian gravity via local deformations of the brane and its metric. The harmonic 'gravity bag' acts as a halo with effective positive energy density. This leads in particular to a significant enhancement of the orbital velocities around galaxies at large distances compared with the Newtonian case, before dropping to zero as the geometry merges with a Milne-like cosmology. Besides these 'harmonic' solutions, there is another class of solutions which is more similar to Einstein gravity. Thus the IKKT model provides an accessible candidate for a quantum theory of gravity.
Lorentz invariant noncommutative algebra for cosmological models coupled to a perfect fluid

Energy Technology Data Exchange (ETDEWEB)

Abreu, Everton M.C.; Marcial, Mateus V.; Mendes, Albert C.R.; Oliveira, Wilson [Universidade Federal Rural do Rio de Janeiro (UFRRJ), Seropedica, RJ (Brazil); Universidade Federal de Juiz de Fora, MG (Brazil)

2013-07-01

Full text: In current theoretical physics there is a relevant number of theoretical investigations that lead to believe that at the first moments of our Universe, the geometry was not commutative and the dominating physics at that time was ruled by the laws of noncommutative (NC) geometry. Therefore, the idea is that the physics of the early moments can be constructed based on these concepts. The first published work using the idea of a NC spacetime were carried out by Snyder who believed that NC principles could make the quantum field theory infinities disappear. However, it did not occur and Snyder's ideas were put to sleep for a long time. The main modern motivations that rekindle the investigation about NC field theories came from string theory and quantum gravity. In the context of quantum mechanics for example, R. Banerjee discussed how NC structures appear in planar quantum mechanics providing a useful way for obtaining them. The analysis was based on the NC algebra used in planar quantum mechanics that was originated from 't Hooft's analysis on dissipation and quantization. In this work we carry out a NC algebra analysis of the Friedmann-Robert-Walker model, coupled to a perfect fluid and in the presence of a cosmological constant. The classical field equations are modified, by the introduction of a shift operator, in order to introduce noncommutativity in these models. (author)
A non-commutative formula for the isotropic magneto-electric response

International Nuclear Information System (INIS)

Leung, Bryan; Prodan, Emil

2013-01-01

A non-commutative formula for the isotropic magneto-electric response of disordered insulators under magnetic fields is derived using the methods of non-commutative geometry. Our result follows from an explicit evaluation of the Ito derivative with respect to the magnetic field of the non-commutative formula for the electric polarization reported in Schulz-Baldes and Teufel (2012 arXiv:1201.4812v1). The quantization, topological invariance and connection to a second Chern number of the magneto-electric response are discussed in the context of three-dimensional, disordered, time-reversal or inversion symmetric topological insulators. (paper)
On the Lie symmetry group for classical fields in noncommutative space

Energy Technology Data Exchange (ETDEWEB)

Pereira, Ricardo Martinho Lima Santiago [Universidade Federal da Bahia (UFBA), BA (Brazil); Instituto Federal da Bahia (IFBA), BA (Brazil); Ressureicao, Caio G. da [Universidade Federal da Bahia (UFBA), BA (Brazil). Inst. de Fisica; Vianna, Jose David M. [Universidade Federal da Bahia (UFBA), BA (Brazil); Universidade de Brasilia (UnB), DF (Brazil)

2011-07-01

Full text: An alternative way to include effects of noncommutative geometries in field theory is based on the concept of noncommutativity among degrees of freedom of the studied system. In this context it is reasonable to consider that, in the multiparticle noncommutative quantum mechanics (NCQM), the noncommutativity among degrees of freedom to discrete system with N particles is also verified. Further, an analysis of the classical limit of the single particle NCQM leads to a deformed Newtonian mechanics where the Newton's second law is modified in order to include the noncommutative parameter {theta}{sub {iota}j} and, for a one-dimensional discrete system with N particles, the dynamical evolution of each particle is given by this modified Newton's second law. Hence, applying the continuous limit to this multiparticle classical system it is possible to obtain a noncommutative extension of two -dimensional field theory in a noncommutative space. In the present communication we consider a noncommutative extension of the scalar field obtained from this approach and we analyze the Lie symmetries in order to compare the Lie group of this field with the usual scalar field in the commutative space. (author)
Stochastic Geometry and Quantum Gravity: Some Rigorous Results

Science.gov (United States)

Zessin, H.

The aim of these lectures is a short introduction into some recent developments in stochastic geometry which have one of its origins in simplicial gravity theory (see Regge Nuovo Cimento 19: 558-571, 1961). The aim is to define and construct rigorously point processes on spaces of Euclidean simplices in such a way that the configurations of these simplices are simplicial complexes. The main interest then is concentrated on their curvature properties. We illustrate certain basic ideas from a mathematical point of view. An excellent representation of this area can be found in Schneider and Weil (Stochastic and Integral Geometry, Springer, Berlin, 2008. German edition: Stochastische Geometrie, Teubner, 2000). In Ambjørn et al. (Quantum Geometry Cambridge University Press, Cambridge, 1997) you find a beautiful account from the physical point of view. More recent developments in this direction can be found in Ambjørn et al. ("Quantum gravity as sum over spacetimes", Lect. Notes Phys. 807. Springer, Heidelberg, 2010). After an informal axiomatic introduction into the conceptual foundations of Regge's approach the first lecture recalls the concepts and notations used. It presents the fundamental zero-infinity law of stochastic geometry and the construction of cluster processes based on it. The second lecture presents the main mathematical object, i.e. Poisson-Delaunay surfaces possessing an intrinsic random metric structure. The third and fourth lectures discuss their ergodic behaviour and present the two-dimensional Regge model of pure simplicial quantum gravity. We terminate with the formulation of basic open problems. Proofs are given in detail only in a few cases. In general the main ideas are developed. Sufficiently complete references are given.
Naked singularities are not singular in distorted gravity

Energy Technology Data Exchange (ETDEWEB)

Garattini, Remo, E-mail: Remo.Garattini@unibg.it [Università degli Studi di Bergamo, Facoltà di Ingegneria, Viale Marconi 5, 24044 Dalmine (Bergamo) (Italy); I.N.F.N. – sezione di Milano, Milan (Italy); Majumder, Barun, E-mail: barunbasanta@iitgn.ac.in [Indian Institute of Technology Gandhinagar, Ahmedabad, Gujarat 382424 (India)

2014-07-15

We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheeler–DeWitt equation. A variational approach is used for the calculation with Gaussian Trial Wave Functionals. The one loop contribution of the graviton to the ZPE is extracted keeping under control the UltraViolet divergences by means of a distorted gravitational field. Two examples of distortion are taken under consideration: Gravity's Rainbow and Noncommutative Geometry. Surprisingly, we find that the ZPE is no more singular when we approach the singularity.
Naked singularities are not singular in distorted gravity

Science.gov (United States)

Garattini, Remo; Majumder, Barun

2014-07-01

We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheele-DeWitt equation. A variational approach is used for the calculation with Gaussian Trial Wave Functionals. The one loop contribution of the graviton to the ZPE is extracted keeping under control the UltraViolet divergences by means of a distorted gravitational field. Two examples of distortion are taken under consideration: Gravity's Rainbow and Noncommutative Geometry. Surprisingly, we find that the ZPE is no more singular when we approach the singularity.
Naked singularities are not singular in distorted gravity

International Nuclear Information System (INIS)

Garattini, Remo; Majumder, Barun

2014-01-01

We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheeler–DeWitt equation. A variational approach is used for the calculation with Gaussian Trial Wave Functionals. The one loop contribution of the graviton to the ZPE is extracted keeping under control the UltraViolet divergences by means of a distorted gravitational field. Two examples of distortion are taken under consideration: Gravity's Rainbow and Noncommutative Geometry. Surprisingly, we find that the ZPE is no more singular when we approach the singularity
Noncommutative Geometry in M-Theory and Conformal Field Theory

International Nuclear Information System (INIS)

Morariu, Bogdan

1999-01-01

In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U q (SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun q (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models
Noncommutative Geometry in M-Theory and Conformal Field Theory

Energy Technology Data Exchange (ETDEWEB)

Morariu, Bogdan [Univ. of California, Berkeley, CA (United States)

1999-05-01

In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U_q(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun_q (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.
Late time acceleration in a non-commutative model of modified cosmology

Energy Technology Data Exchange (ETDEWEB)

Malekolkalami, B., E-mail: b.malakolkalami@uok.ac.ir [Department of Physics, University of Kurdistan, Pasdaran St., Sanandaj (Iran, Islamic Republic of); Atazadeh, K., E-mail: atazadeh@azaruniv.ac.ir [Department of Physics, Azarbaijan Shahid Madani University, 53714-161, Tabriz (Iran, Islamic Republic of); Vakili, B., E-mail: b-vakili@iauc.ac.ir [Department of Physics, Central Tehran Branch, Islamic Azad University, Tehran (Iran, Islamic Republic of)

2014-12-12

We investigate the effects of non-commutativity between the position–position, position–momentum and momentum–momentum of a phase space corresponding to a modified cosmological model. We show that the existence of such non-commutativity results in a Moyal Poisson algebra between the phase space variables in which the product law between the functions is of the kind of an α-deformed product. We then transform the variables in such a way that the Poisson brackets between the dynamical variables take the form of a usual Poisson bracket but this time with a noncommutative structure. For a power law expression for the function of the Ricci scalar with which the action of the gravity model is modified, the exact solutions in the commutative and noncommutative cases are presented and compared. In terms of these solutions we address the issue of the late time acceleration in cosmic evolution.
Late time acceleration in a non-commutative model of modified cosmology

International Nuclear Information System (INIS)

Malekolkalami, B.; Atazadeh, K.; Vakili, B.

2014-01-01

We investigate the effects of non-commutativity between the position–position, position–momentum and momentum–momentum of a phase space corresponding to a modified cosmological model. We show that the existence of such non-commutativity results in a Moyal Poisson algebra between the phase space variables in which the product law between the functions is of the kind of an α-deformed product. We then transform the variables in such a way that the Poisson brackets between the dynamical variables take the form of a usual Poisson bracket but this time with a noncommutative structure. For a power law expression for the function of the Ricci scalar with which the action of the gravity model is modified, the exact solutions in the commutative and noncommutative cases are presented and compared. In terms of these solutions we address the issue of the late time acceleration in cosmic evolution
Quantum Gravity and Cosmology: an intimate interplay

Science.gov (United States)

Sakellariadou, Mairi

2017-08-01

I will briefly discuss three cosmological models built upon three distinct quantum gravity proposals. I will first highlight the cosmological rôle of a vector field in the framework of a string/brane cosmological model. I will then present the resolution of the big bang singularity and the occurrence of an early era of accelerated expansion of a geometric origin, in the framework of group field theory condensate cosmology. I will then summarise results from an extended gravitational model based on non-commutative spectral geometry, a model that offers a purely geometric explanation for the standard model of particle physics.

A new approach for gravity localization in six-dimensional geometries

International Nuclear Information System (INIS)

Santos, Victor Pereira do Nascimento; Almeida, Carlos Alberto Santos de

2011-01-01

Full text: The idea that spacetime may have more than four dimensions is old, originally presented as an attempt to unify Maxwell's theory of Electromagnetism with the brand-new gravitation theory of Einstein. Such extra dimensions are in principle unobservable to the energy scales currently available. However, its effects can be seen in short distance gravity experiments and in observations in cosmology. Also, it is used as a mechanism to explain the difference between the energy scales of the weak force and gravity, which is called the hierarchy problem. The current framework for the extra dimension scenario is consider the four-dimensional known universe as embedded in a higher dimensional space called bulk. The form of this bulk determines how we perceive gravity in our universe; then, the behaviour of gravitational field depends on the geometry of the bulk. Metric solutions were already presented for string-like defect, with and without matter sources, where was shown that the gravity Newtonian potential grows with the inverse cube of distance. Such correction arises from a very particular mass spectrum for the gravitational field, which already contains the orbital angular momentum contributions. In this work we study the behaviour of gravitational field in a extra-dimensional braneworld scenario, using non-factorizable geometries (which preserves Poincare symmetry) and setting suitable matter distributions in order to verify its localization, for several geometries. For such geometries it is possible to find explicit solutions for the tensor fluctuations of the metric. (author)
q-deformation and semidualization in 3D quantum gravity

Energy Technology Data Exchange (ETDEWEB)

Majid, S [School of Mathematical Sciences, Queen Mary, University of London, 327 Mile End Rd, London E1 4NS (United Kingdom); Schroers, B J [Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom)], E-mail: s.majid@qmul.ac.uk, E-mail: bernd@ma.hw.ac.uk

2009-10-23

We explore in detail the role in euclidean 3D quantum gravity of quantum Born reciprocity or 'semidualization'. The latter is an algebraic operation defined using quantum group methods that interchanges position and momentum. Using this we are able to clarify the structural relationships between the effective noncommutative geometries that have been discussed in the context of 3D gravity. We show that the spin model based on D(U(su{sub 2})) for quantum gravity without cosmological constant is the semidual of a quantum particle on a 3-sphere, while the bicrossproduct (DSR) model is the semidual of a quantum particle on hyperbolic space. We show further how the different models are all specific limits of q-deformed models with q=e{sup -{Dirac_h}}{sup {radical}}{sup (-{lambda})/m{sub p}}, where m{sub p} is the Planck mass and {lambda} is the cosmological constant, and argue that semidualization interchanges m{sub p} {r_reversible} l{sub c}, where l{sub c} is the cosmological length scale l{sub c}=1/{radical}(|{lambda}|). We investigate the physics of semidualization by studying representation theory. In both the spin model and its semidual we show that irreducible representations have a physical picture as solutions of a respectively noncommutative/curved wave equation. We explain, moreover, that the q-deformed model, at a certain algebraic level, is self-dual under semidualization.
Towards Noncommutative Topological Quantum Field Theory: Tangential Hodge-Witten cohomology

International Nuclear Information System (INIS)

Zois, I P

2014-01-01

Some years ago we initiated a program to define Noncommutative Topological Quantum Field Theory (see [1]). The motivation came both from physics and mathematics: On the one hand, as far as physics is concerned, following the well-known holography principle of 't Hooft (which in turn appears essentially as a generalisation of the Hawking formula for black hole entropy), quantum gravity should be a topological quantum field theory. On the other hand as far as mathematics is concerned, the motivation came from the idea to replace the moduli space of flat connections with the Gabai moduli space of codim-1 taut foliations for 3 dim manifolds. In most cases the later is finite and much better behaved and one might use it to define some version of Donaldson-Floer homology which, hopefully, would be easier to compute. The use of foliations brings noncommutative geometry techniques immediately into the game. The basic tools are two: Cyclic cohomology of the corresponding foliation C*-algebra and the so called ''tangential cohomology'' of the foliation. A necessary step towards this goal is to develop some sort of Hodge theory both for cyclic (and Hochschild) cohomology and for tangential cohomology. Here we present a method to develop a Hodge theory for tangential cohomology of foliations by mimicing Witten's approach to ordinary Morse theory by perturbations of the Laplacian
Nonabelian noncommutative gauge theory via noncommutative extra dimensions

Energy Technology Data Exchange (ETDEWEB)

Jurco, Branislav E-mail: jurco@theorie.physik.uni-muenchen.de; Schupp, Peter E-mail: schupp@theorie.physik.uni-muenchen.de; Wess, Julius E-mail: wess@theorie.physik.uni-muenchen.de

2001-06-18

The concept of covariant coordinates on noncommutative spaces leads directly to gauge theories with generalized noncommutative gauge fields of the type that arises in string theory with background B-fields. The theory is naturally expressed in terms of cochains in an appropriate cohomology; we discuss how it fits into the framework of projective modules. The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map). As application we show the exact equality of the Dirac-Born-Infeld action with B-field in the commutative setting and its semi-noncommutative cousin in the intermediate picture. Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; an explicit map between abelian and nonabelian gauge fields is given. All constructions are also valid for non-constant B-field, Poisson structure and metric.
Nonabelian noncommutative gauge theory via noncommutative extra dimensions

International Nuclear Information System (INIS)

Jurco, Branislav; Schupp, Peter; Wess, Julius

2001-01-01

The concept of covariant coordinates on noncommutative spaces leads directly to gauge theories with generalized noncommutative gauge fields of the type that arises in string theory with background B-fields. The theory is naturally expressed in terms of cochains in an appropriate cohomology; we discuss how it fits into the framework of projective modules. The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map). As application we show the exact equality of the Dirac-Born-Infeld action with B-field in the commutative setting and its semi-noncommutative cousin in the intermediate picture. Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; an explicit map between abelian and nonabelian gauge fields is given. All constructions are also valid for non-constant B-field, Poisson structure and metric
Anomalous dimension in three-dimensional semiclassical gravity

International Nuclear Information System (INIS)

Alesci, Emanuele; Arzano, Michele

2012-01-01

The description of the phase space of relativistic particles coupled to three-dimensional Einstein gravity requires momenta which are coordinates on a group manifold rather than on ordinary Minkowski space. The corresponding field theory turns out to be a non-commutative field theory on configuration space and a group field theory on momentum space. Using basic non-commutative Fourier transform tools we introduce the notion of non-commutative heat-kernel associated with the Laplacian on the non-commutative configuration space. We show that the spectral dimension associated to the non-commutative heat kernel varies with the scale reaching a non-integer value smaller than three for Planckian diffusion scales.
Existence of stable wormholes on a non-commutative-geometric background in modified gravity

Energy Technology Data Exchange (ETDEWEB)

Zubair, M.; Mustafa, G. [COMSATS, Institute of Information Technology, Department of Mathematics, Lahore (Pakistan); Waheed, Saira [Prince Mohammad Bin Fahd University, Al Khobar (Saudi Arabia); Abbas, G. [The Islamia University of Bahawalpur, Department of Mathematics, Bahawalpur (Pakistan)

2017-10-15

In this paper, we discuss spherically symmetric wormhole solutions in f(R, T) modified theory of gravity by introducing well-known non-commutative geometry in terms of Gaussian and Lorentzian distributions of string theory. For analytic discussion, we consider an interesting model of f(R, T) gravity defined by f(R, T) = f{sub 1}(R) + λT. By taking two different choices for the function f{sub 1}(R), that is, f{sub 1}(R) = R and f{sub 1}(R) = R + αR{sup 2} + γR{sup n}, we discuss the possible existence of wormhole solutions. In the presence of non-commutative Gaussian and Lorentzian distributions, we get exact and numerical solutions for both these models. By taking appropriate values of the free parameters, we discuss different properties of these wormhole models analytically and graphically. Further, using an equilibrium condition, it is found that these solutions are stable. Also, we discuss the phenomenon of gravitational lensing for the exact wormhole model and it is found that the deflection angle diverges at the wormhole throat. (orig.)
The DSR-deformed relativistic symmetries and the relative locality of 3D quantum gravity

International Nuclear Information System (INIS)

Amelino-Camelia, Giovanni; Arzano, Michele; Bianco, Stefano; Buonocore, Riccardo J

2013-01-01

Over the last decade there were significant advances in the understanding of quantum gravity coupled to point particles in 3D ((2+1)-dimensional) spacetime. Most notably it is emerging that the theory can be effectively described as a theory of free particles on a momentum space with anti-deSitter geometry and with noncommutative spacetime coordinates of the type [x μ , x ν ] = iℏℓε μν ρ x ρ . We here show that the recently proposed relative-locality curved-momentum-space framework is ideally suited for accommodating these structures' characteristics of 3D quantum gravity. Through this we obtain an intuitive characterization of the DSR-deformed Poincaré symmetries of 3D quantum gravity, and find that the associated relative spacetime locality is of the type producing dual-gravity lensing. (paper)
Non-topological non-commutativity in string theory

International Nuclear Information System (INIS)

Guttenberg, S.; Herbst, M.; Kreuzer, M.; Rashkov, R.

2008-01-01

Quantization of coordinates leads to the non-commutative product of deformation quantization, but is also at the roots of string theory, for which space-time coordinates become the dynamical fields of a two-dimensional conformal quantum field theory. Appositely, open string diagrams provided the inspiration for Kontsevich's solution of the long-standing problem of quantization of Poisson geometry by virtue of his formality theorem. In the context of D-brane physics non-commutativity is not limited, however, to the topological sector. We show that non-commutative effective actions still make sense when associativity is lost and establish a generalized Connes-Flato-Sternheimer condition through second order in a derivative expansion. The measure in general curved backgrounds is naturally provided by the Born-Infeld action and reduces to the symplectic measure in the topological limit, but remains non-singular even for degenerate Poisson structures. Analogous superspace deformations by RR-fields are also discussed. (Abstract Copyright [2008], Wiley Periodicals, Inc.)
Spectral theorem in noncommutative field theories: Jacobi dynamics

International Nuclear Information System (INIS)

Géré, Antoine; Wallet, Jean-Christophe

2015-01-01

Jacobi operators appear as kinetic operators of several classes of noncommutative field theories (NCFT) considered recently. This paper deals with the case of bounded Jacobi operators. A set of tools mainly issued from operator and spectral theory is given in a way applicable to the study of NCFT. As an illustration, this is applied to a gauge-fixed version of the induced gauge theory on the Moyal plane expanded around a symmetric vacuum. The characterization of the spectrum of the kinetic operator is given, showing a behavior somewhat similar to a massless theory. An attempt to characterize the noncommutative geometry related to the gauge fixed action is presented. Using a Dirac operator obtained from the kinetic operator, it is shown that one can construct an even, regular, weakly real spectral triple. This spectral triple does not define a noncommutative metric space for the Connes spectral distance. (paper)
Nonperturbative studies of quantum field theories on noncommutative spaces

International Nuclear Information System (INIS)

Volkholz, J.

2007-01-01

This work deals with three quantum field theories on spaces with noncommuting position operators. Noncommutative models occur in the study of string theories and quantum gravity. They usually elude treatment beyond the perturbative level. Due to the technique of dimensional reduction, however, we are able to investigate these theories nonperturbatively. This entails translating the action functionals into a matrix language, which is suitable for numerical simulations. First we explore the λφ 4 model on a noncommutative plane. We investigate the continuum limit at fixed noncommutativity, which is known as the double scaling limit. Here we focus especially on the fate of the striped phase, a phase peculiar to the noncommutative version of the regularized λφ 4 model. We find no evidence for its existence in the double scaling limit. Next we examine the U(1) gauge theory on a four-dimensional spacetime, where two spatial directions are noncommutative. We examine the phase structure and find a new phase with a spontaneously broken translation symmetry. In addition we demonstrate the existence of a finite double scaling limit which confirms the renormalizability of the theory. Furthermore we investigate the dispersion relation of the photon. In the weak coupling phase our results are consistent with an infrared instability predicted by perturbation theory. If the translational symmetry is broken, however, we find a dispersion relation corresponding to a massless particle. Finally, we investigate a supersymmetric theory on the fuzzy sphere, which features scalar neutral bosons and Majorana fermions. The supersymmetry is exact in the limit of infinitely large matrices. We investigate the phase structure of the model and find three distinct phases. Summarizing, we study noncommutative field theories beyond perturbation theory. Moreover, we simulate a supersymmetric theory on the fuzzy sphere, which might provide an alternative to attempted lattice formulations. (orig.)
Nonperturbative studies of quantum field theories on noncommutative spaces

Energy Technology Data Exchange (ETDEWEB)

Volkholz, J.

2007-11-16

This work deals with three quantum field theories on spaces with noncommuting position operators. Noncommutative models occur in the study of string theories and quantum gravity. They usually elude treatment beyond the perturbative level. Due to the technique of dimensional reduction, however, we are able to investigate these theories nonperturbatively. This entails translating the action functionals into a matrix language, which is suitable for numerical simulations. First we explore the {lambda}{phi}{sup 4} model on a noncommutative plane. We investigate the continuum limit at fixed noncommutativity, which is known as the double scaling limit. Here we focus especially on the fate of the striped phase, a phase peculiar to the noncommutative version of the regularized {lambda}{phi}{sup 4} model. We find no evidence for its existence in the double scaling limit. Next we examine the U(1) gauge theory on a four-dimensional spacetime, where two spatial directions are noncommutative. We examine the phase structure and find a new phase with a spontaneously broken translation symmetry. In addition we demonstrate the existence of a finite double scaling limit which confirms the renormalizability of the theory. Furthermore we investigate the dispersion relation of the photon. In the weak coupling phase our results are consistent with an infrared instability predicted by perturbation theory. If the translational symmetry is broken, however, we find a dispersion relation corresponding to a massless particle. Finally, we investigate a supersymmetric theory on the fuzzy sphere, which features scalar neutral bosons and Majorana fermions. The supersymmetry is exact in the limit of infinitely large matrices. We investigate the phase structure of the model and find three distinct phases. Summarizing, we study noncommutative field theories beyond perturbation theory. Moreover, we simulate a supersymmetric theory on the fuzzy sphere, which might provide an alternative to attempted
Reconstruction of the spontaneously broken gauge theory in non-commutative geometry

International Nuclear Information System (INIS)

Okumura, Y.; Morita, K.

1996-01-01

The scheme previously proposed by the present authors is modified to incorporate the strong interaction by affording the direct product internal symmetry. The authors do not need to prepare the extra discrete space for the colour gauge group responsible for the strong interaction to reconstruct the standard model and the left-right symmetric gauge model (LRSM). The approach based on non-commutative geometry leads us to present many attractive points such as the unified picture of the gauge and Higgs field as the generalized connection on the discrete space M 4 x Z N . This approach leads to unified picture of gauge and Higgs fields as the generalized connection. The standard model needs N=2 discrete space for reconstruction in this formalism. LRSM is still alive as a model with the intermediate symmetry of the spontaneously broken SO(10) grand unified theory (GUT). N=3 discrete space is needed for the reconstruction of LRSM to include two Higgs φ and ξ bosons usual transformed as (2, 2 * , 0) and (1, 3, -2) under SU(2) L x SU(2) R x U(1) Y , respectively. ξ is responsible to make v R Majorana fermion and so well explains the seesaw mechanism. Up and down quarks have different masses through the vacuum expectation value of φ
Non-commutative representation for quantum systems on Lie groups

Energy Technology Data Exchange (ETDEWEB)

Raasakka, Matti Tapio

2014-01-27

space path integral with the help of the non-commutative dual variables. In studying the classical limit of the path integral, we show that we recover the correct classical equations of motion for the particle, if we account for the deformation of the phase space in the variational calculus. The non-commutative variables correspond in this limit to the classical momentum variables, further verifying their physical interpretation. We conclude that the non-commutative harmonic analysis facilitates a convenient study of the classical limit of quantum dynamics on a Lie group even if the group is compact, in which case variational calculus cannot easily be applied. As the second physics application, we repeat our above considerations for the case of Ponzano-Regge spin foam model for 3-dimensional quantum gravity. The non-commutative dual variables correspond in this case to discrete metric variables, thus illuminating the geometrical interpretation of the model. Again, we find that a convenient study of the classical limit is made possible through the non-commutative phase space path integral.
Non-commutative representation for quantum systems on Lie groups

International Nuclear Information System (INIS)

Raasakka, Matti Tapio

2014-01-01

integral with the help of the non-commutative dual variables. In studying the classical limit of the path integral, we show that we recover the correct classical equations of motion for the particle, if we account for the deformation of the phase space in the variational calculus. The non-commutative variables correspond in this limit to the classical momentum variables, further verifying their physical interpretation. We conclude that the non-commutative harmonic analysis facilitates a convenient study of the classical limit of quantum dynamics on a Lie group even if the group is compact, in which case variational calculus cannot easily be applied. As the second physics application, we repeat our above considerations for the case of Ponzano-Regge spin foam model for 3-dimensional quantum gravity. The non-commutative dual variables correspond in this case to discrete metric variables, thus illuminating the geometrical interpretation of the model. Again, we find that a convenient study of the classical limit is made possible through the non-commutative phase space path integral.
Extended Equivalence Principle: Implications for Gravity, Geometry and Thermodynamics

OpenAIRE

Sivaram, C.; Arun, Kenath

2012-01-01

The equivalence principle was formulated by Einstein in an attempt to extend the concept of inertial frames to accelerated frames, thereby bringing in gravity. In recent decades, it has been realised that gravity is linked not only with geometry of space-time but also with thermodynamics especially in connection with black hole horizons, vacuum fluctuations, dark energy, etc. In this work we look at how the equivalence principle manifests itself in these different situations where we have str...
Towards Noncommutative Topological Quantum Field Theory – Hodge theory for cyclic cohomology

International Nuclear Information System (INIS)

Zois, I P

2014-01-01

Some years ago we initiated a program to define Noncommutative Topological Quantum Field Theory (see [1]). The motivation came both from physics and mathematics: On the one hand, as far as physics is concerned, following the well-known holography principle of 't Hooft (which in turn appears essentially as a generalisation of the Hawking formula for black hole entropy), quantum gravity should be a topological quantum field theory. On the other hand as far as mathematics is concerned, the motivation came from the idea to replace the moduli space of flat connections with the Gabai moduli space of codim-1 taut foliations for 3 dim manifolds. In most cases the later is finite and much better behaved and one might use it to define some version of Donaldson-Floer homology which, hopefully, would be easier to compute. The use of foliations brings noncommutative geometry techniques immediately into the game. The basic tools are two: Cyclic cohomology of the corresponding foliation C*-algebra and the so called ''tangential cohomology'' of the foliation. A necessary step towards this goal is to develop some sort of Hodge theory both for cyclic (and Hochschild) cohomology and for tangential cohomology. Here we present a method to develop a Hodge theory for cyclic and Hochschild cohomology for the corresponding C*-algebra of a foliation
Noncommutative spaces and matrix embeddings on flat ℝ{sup 2n+1}

Energy Technology Data Exchange (ETDEWEB)

Karczmarek, Joanna L.; Yeh, Ken Huai-Che [Department of Physics and Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver (Canada)

2015-11-23

We conjecture an embedding operator which assigns, to any 2n+1 hermitian matrices, a 2n-dimensional hypersurface in flat (2n+1)-dimensional Euclidean space. This corresponds to precisely defining a fuzzy D(2n)-brane corresponding to N D0-branes. Points on the emergent hypersurface correspond to zero eigenstates of the embedding operator, which have an interpretation as coherent states underlying the emergent noncommutative geometry. Using this correspondence, all physical properties of the emergent D(2n)-brane can be computed. We apply our conjecture to noncommutative flat and spherical spaces. As a by-product, we obtain a construction of a rotationally symmetric flat noncommutative space in 4 dimensions.
Null geodesics and red-blue shifts of photons emitted from geodesic particles around a noncommutative black hole space-time

Science.gov (United States)

Kuniyal, Ravi Shankar; Uniyal, Rashmi; Biswas, Anindya; Nandan, Hemwati; Purohit, K. D.

2018-06-01

We investigate the geodesic motion of massless test particles in the background of a noncommutative geometry-inspired Schwarzschild black hole. The behavior of effective potential is analyzed in the equatorial plane and the possible motions of massless particles (i.e. photons) for different values of impact parameter are discussed accordingly. We have also calculated the frequency shift of photons in this space-time. Further, the mass parameter of a noncommutative inspired Schwarzschild black hole is computed in terms of the measurable redshift of photons emitted by massive particles moving along circular geodesics in equatorial plane. The strength of gravitational fields of noncommutative geometry-inspired Schwarzschild black hole and usual Schwarzschild black hole in General Relativity is also compared.
Non-commuting variations in mathematics and physics a survey

CERN Document Server

Preston, Serge

2016-01-01

This text presents and studies the method of so –called noncommuting variations in Variational Calculus. This method was pioneered by Vito Volterra who noticed that the conventional Euler-Lagrange (EL-) equations are not applicable in Non-Holonomic Mechanics and suggested to modify the basic rule used in Variational Calculus. This book presents a survey of Variational Calculus with non-commutative variations and shows that most basic properties of conventional Euler-Lagrange Equations are, with some modifications, preserved for EL-equations with K-twisted (defined by K)-variations. Most of the book can be understood by readers without strong mathematical preparation (some knowledge of Differential Geometry is necessary). In order to make the text more accessible the definitions and several necessary results in Geometry are presented separately in Appendices I and II Furthermore in Appendix III a short presentation of the Noether Theorem describing the relation between the symmetries of the differential equa...

Stringy Fuzziness as the Custodial of Time-Space Noncommutativity

CERN Document Server

Barbón, José L F

2000-01-01

We study aspects of obtaining field theories with noncommuting time-space coordinates as limits of open-string theories in constant electric-field backgrounds. We find that, within the standard closed-string backgrounds, there is an obstruction to decoupling the time-space noncommutativity scale from that of the string fuzziness scale. We speculate that this censorship may be string-theory's way of protecting the causality and unitarity structure. We study the moduli space of the obstruction in terms of the open- and closed-string backgrounds. Cases of both zero and infinite brane tensions as well as zero string couplings are obtained. A decoupling can be achieved formally by considering complex values of the dilaton and inverting the role of space and time of the light cone. This is reminiscent of a black-hole horizon. We study the corresponding supergravity solution in the large-N limit and find that the geometry has a naked singularity at the physical scale of noncommutativity.
Stringy fuzziness as the custodian of time-space noncommutativity

CERN Document Server

Barbón, José L F

2000-01-01

We study aspects of obtaining field theories with noncommuting time- space coordinates as limits of open-string theories in constant electric-field backgrounds. We find that, within the standard closed- string backgrounds, there is an obstruction to decoupling the time- space noncommutativity scale from that of the string fuzziness scale. We speculate that this censorship may be string-theory's way of protecting the causality and unitarity structure. We study the moduli space of the obstruction in terms of the open- and closed-string backgrounds. Cases of both zero and infinite brane tensions as well as zero string couplings are obtained. A decoupling can be achieved formally by considering complex values of the dilaton and inverting the role of space and time in the light cone. This is reminiscent of a black-hole horizon. We study the corresponding supergravity solution in the large-N limit and find that the geometry has a naked singularity at the physical scale of noncommutativity. (23 refs).
Noncommutative unification of general relativity and quantum mechanics

International Nuclear Information System (INIS)

Heller, Michael; Pysiak, Leszek; Sasin, Wieslaw

2005-01-01

We present a model unifying general relativity and quantum mechanics based on a noncommutative geometry. This geometry is developed in terms of a noncommutative algebra A which is defined on a transformation groupoid Γ given by the action of a noncompact group G on the total space E of a principal fiber bundle over space-time M. The case is important since to obtain physical effects predicted by the model we should assume that G is a Lorentz group or some of its representations. We show that the generalized Einstein equation of the model has the form of the eigenvalue equation for the generalized Ricci operator, and all relevant operators in the quantum sector of the model are random operators; we study their dynamics. We also show that the model correctly reproduces general relativity and the usual quantum mechanics. It is interesting that the latter is recovered by performing the measurement of any observable. In the act of such a measurement the model 'collapses' to the usual quantum mechanics
Renormalization group equations and the Lifshitz point in noncommutative Landau-Ginsburg theory

International Nuclear Information System (INIS)

Chen, G.-H.; Wu, Y.-S.

2002-01-01

A one-loop renormalization group (RG) analysis is performed for noncommutative Landau-Ginsburg theory in an arbitrary dimension. We adopt a modern version of the Wilsonian RG approach, in which a shell integration in momentum space bypasses the potential IR singularities due to UV-IR mixing. The momentum-dependent trigonometric factors in interaction vertices, characteristic of noncommutative geometry, are marginal under RG transformations, and their marginality is preserved at one loop. A negative Θ-dependent anomalous dimension is discovered as a novel effect of the UV-IR mixing. We also found a noncommutative Wilson-Fisher (NCWF) fixed point in less than four dimensions. At large noncommutativity, a momentum space instability is induced by quantum fluctuations, and a consequential first-order phase transition is identified together with a Lifshitz point in the phase diagram. In the vicinity of the Lifshitz point, we introduce two critical exponents ν m and β k , whose values are determined to be 1/4 and 1/2, respectively, at mean-field level
Essay on physics and non-commutative geometry

International Nuclear Information System (INIS)

Connes, A.

1990-01-01

Our aim, in this article, is to try to discover what physics would be like if the space in which it took place was not a set of points, but a non-commutative space. We shall not go very far in this direction, and the consequences of this investigation are for the moment either mathematical or only applied to a commutative space-time. It is clear, however, that a tool as remarkable as the Dixmier trace for analyzing logarithmic divergences should be useful to physicists. Moreover we have been able to show that a small modification of our picture of space-time gives a conceptual explanation of the Higgs fields and of the way they appear in the Weinberg-Salam model. This should allow us to make at the classical level explicit predictions of the Higgs mass: a very crude one is discussed. (author)
Noncommutative Lagrange Mechanics

Directory of Open Access Journals (Sweden)

Denis Kochan

2008-02-01

Full Text Available It is proposed how to impose a general type of ''noncommutativity'' within classical mechanics from first principles. Formulation is performed in completely alternative way, i.e. without any resort to fuzzy and/or star product philosophy, which are extensively applied within noncommutative quantum theories. Newton-Lagrange noncommutative equations of motion are formulated and their properties are analyzed from the pure geometrical point of view. It is argued that the dynamical quintessence of the system consists in its kinetic energy (Riemannian metric specifying Riemann-Levi-Civita connection and thus the inertia geodesics of the free motion. Throughout the paper, ''noncommutativity'' is considered as an internal geometric structure of the configuration space, which can not be ''observed'' per se. Manifestation of the noncommutative phenomena is mediated by the interaction of the system with noncommutative background under the consideration. The simplest model of the interaction (minimal coupling is proposed and it is shown that guiding affine connection is modified by the quadratic analog of the Lorentz electromagnetic force (contortion term.
Hyperunified field theory and gravitational gauge-geometry duality

International Nuclear Information System (INIS)

Wu, Yue-Liang

2018-01-01

A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D h - 1). The dimension D h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond. (orig.)
Hyperunified field theory and gravitational gauge-geometry duality

Energy Technology Data Exchange (ETDEWEB)

Wu, Yue-Liang [International Centre for Theoretical Physics Asia-Pacific (ICTP-AP), Beijing (China); Chinese Academy of Sciences, Institute of Theoretical Physics, Beijing (China); University of Chinese Academy of Sciences (UCAS), Beijing (China)

2018-01-15

A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D{sub h} - 1). The dimension D{sub h} of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond. (orig.)
Hyperunified field theory and gravitational gauge-geometry duality

Science.gov (United States)

Wu, Yue-Liang

2018-01-01

A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D_h-1). The dimension D_h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond.
Noncommutative field gas driven inflation

Energy Technology Data Exchange (ETDEWEB)

Barosi, Luciano; Brito, Francisco A [Departamento de Fisica, Universidade Federal de Campina Grande, Caixa Postal 10071, 58109-970 Campina Grande, Paraiba (Brazil); Queiroz, Amilcar R, E-mail: lbarosi@ufcg.edu.br, E-mail: fabrito@df.ufcg.edu.br, E-mail: amilcarq@gmail.com [Centro Internacional de Fisica da Materia Condensada, Universidade de Brasilia, Caixa Postal 04667, Brasilia, DF (Brazil)

2008-04-15

We investigate early time inflationary scenarios in a Universe filled with a dilute noncommutative bosonic gas at high temperature. A noncommutative bosonic gas is a gas composed of a bosonic scalar field with noncommutative field space on a commutative spacetime. Such noncommutative field theories were recently introduced as a generalization of quantum mechanics on a noncommutative spacetime. Key features of these theories are Lorentz invariance violation and CPT violation. In the present study we use a noncommutative bosonic field theory that, besides the noncommutative parameter {theta}, shows up a further parameter {sigma}. This parameter {sigma} controls the range of the noncommutativity and acts as a regulator for the theory. Both parameters play a key role in the modified dispersion relations of the noncommutative bosonic field, leading to possible striking consequences for phenomenology. In this work we obtain an equation of state p = {omega}({sigma},{theta};{beta}){rho} for the noncommutative bosonic gas relating pressure p and energy density {rho}, in the limit of high temperature. We analyse possible behaviours for these gas parameters {sigma}, {theta} and {beta}, so that -1{<=}{omega}<-1/3, which is the region where the Universe enters an accelerated phase.
Noncommutative black holes

Energy Technology Data Exchange (ETDEWEB)

Lopez-DomInguez, J C [Instituto de Fisica de la Universidad de Guanajuato PO Box E-143, 37150 Leoen Gto. (Mexico); Obregon, O [Instituto de Fisica de la Universidad de Guanajuato PO Box E-143, 37150 Leoen Gto. (Mexico); RamIrez, C [Facultad de Ciencias FIsico Matematicas, Universidad Autonoma de Puebla, PO Box 1364, 72000 Puebla (Mexico); Sabido, M [Instituto de Fisica de la Universidad de Guanajuato PO Box E-143, 37150 Leoen Gto. (Mexico)

2007-11-15

We study noncommutative black holes, by using a diffeomorphism between the Schwarzschild black hole and the Kantowski-Sachs cosmological model, which is generalized to noncommutative minisuperspace. Through the use of the Feynman-Hibbs procedure we are able to study the thermodynamics of the black hole, in particular, we calculate Hawking's temperature and entropy for the 'noncommutative' Schwarzschild black hole.
Prime divisors and noncommutative valuation theory

CERN Document Server

Marubayashi, Hidetoshi

2012-01-01

Classical valuation theory has applications in number theory and class field theory as well as in algebraic geometry, e.g. in a divisor theory for curves. But the noncommutative equivalent is mainly applied to finite dimensional skewfields. Recently however, new types of algebras have become popular in modern algebra; Weyl algebras, deformed and quantized algebras, quantum groups and Hopf algebras, etc. The advantage of valuation theory in the commutative case is that it allows effective calculations, bringing the arithmetical properties of the ground field into the picture. This arithmetical nature is also present in the theory of maximal orders in central simple algebras. Firstly, we aim at uniting maximal orders, valuation rings, Dubrovin valuations, etc. in a common theory, the theory of primes of algebras. Secondly, we establish possible applications of the noncommutative arithmetics to interesting classes of algebras, including the extension of central valuations to nice classes of quantized a...
Géométrie non-commutative, théorie de jauge et renormalisation

OpenAIRE

De Goursac , Axel

2009-01-01

Thèse effectuée en cotutelle au Département de Mathématique de l'Université de Münster (Allemagne); Nowadays, noncommutative geometry is a growing domain of mathematics, which can appear as a promising framework for modern physics. Quantum field theories on "noncommutative spaces" are indeed much investigated, and suffer from a new type of divergence called the ultraviolet-infrared mixing. However, this problem has recently been solved by H. Grosse and R. Wulkenhaar by adding to the action of...
Cosmological production of noncommutative black holes

International Nuclear Information System (INIS)

Mann, Robert B.; Nicolini, Piero

2011-01-01

We investigate the pair creation of noncommutative black holes in a background with a positive cosmological constant. As a first step we derive the noncommutative geometry inspired Schwarzschild-de Sitter solution. By varying the mass and the cosmological constant parameters, we find several spacetimes compatible with the new solution: positive-mass spacetimes admit one cosmological horizon and two, one, or no black hole horizons, while negative-mass spacetimes have just a cosmological horizon. These new black holes share the properties of the corresponding asymptotically flat solutions, including the nonsingular core and thermodynamic stability in the final phase of the evaporation. As a second step we determine the action which generates the matter sector of gravitational field equations and we construct instantons describing the pair production of black holes and the other admissible topologies. As a result we find that for current values of the cosmological constant the de Sitter background is quantum mechanically stable according to experience. However, positive-mass noncommutative black holes and solitons would have plentifully been produced during inflationary times for Planckian values of the cosmological constant. As a special result we find that, in these early epochs of the Universe, Planck size black holes production would have been largely disfavored. We also find a potential instability for production of negative-mass solitons.
Perturbed nonlinear models from noncommutativity

International Nuclear Information System (INIS)

Cabrera-Carnero, I.; Correa-Borbonet, Luis Alejandro; Valadares, G.C.S.

2007-01-01

By means of the Ehrenfest's Theorem inside the context of a noncommutative Quantum Mechanics it is obtained the Newton's Second Law in noncommutative space. Considering discrete systems with infinite degrees of freedom whose dynamical evolutions are governed by the noncommutative Newton's Second Law we have constructed some alternative noncommutative generalizations of two-dimensional field theories. (author)
Quantum mechanics on noncommutative spacetime

International Nuclear Information System (INIS)

Calmet, Xavier; Selvaggi, Michele

2006-01-01

We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a nonrelativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical noncommutative spacetime. An interesting new feature of quantum mechanics formulated on a noncommutative spacetime is an intrinsic electric dipole moment. We note, however, that noncommutative intrinsic dipole moments are not observable in present experiments searching for an electric dipole moment of leptons or nuclei such as the neutron since they are spin independent. These experiments are sensitive to the energy difference between two states and the noncommutative effect thus cancels out. Bounds on the noncommutative scale found in the literature relying on such intrinsic electric dipole moments are thus incorrect
Noncommutative baby Skyrmions

International Nuclear Information System (INIS)

Ioannidou, Theodora; Lechtenfeld, Olaf

2009-01-01

We subject the baby Skyrme model to a Moyal deformation, for unitary or Grassmannian target spaces and without a potential term. In the Abelian case, the radial BPS configurations of the ordinary noncommutative sigma model also solve the baby Skyrme equation of motion. This gives a class of exact analytic noncommutative baby Skyrmions, which have a singular commutative limit but are stable against scaling due to the noncommutativity. We compute their energies, investigate their stability and determine the asymptotic two-Skyrmion interaction.
Information theory, spectral geometry, and quantum gravity.

Science.gov (United States)

Kempf, Achim; Martin, Robert

2008-01-18

We show that there exists a deep link between the two disciplines of information theory and spectral geometry. This allows us to obtain new results on a well-known quantum gravity motivated natural ultraviolet cutoff which describes an upper bound on the spatial density of information. Concretely, we show that, together with an infrared cutoff, this natural ultraviolet cutoff beautifully reduces the path integral of quantum field theory on curved space to a finite number of ordinary integrations. We then show, in particular, that the subsequent removal of the infrared cutoff is safe.
S-duality and noncommutative gauge theory

International Nuclear Information System (INIS)

Gopakumar, R.; Maldacena, J.; Minwalla, S.; Strominger, A.

2000-01-01

It is conjectured that strongly coupled, spatially noncommutative CN=4 Yang-Mills theory has a dual description as a weakly coupled open string theory in a near critical electric field, and that this dual theory is fully decoupled from closed strings. Evidence for this conjecture is given by the absence of physical closed string poles in the non-planar one-loop open string diagram. The open string theory can be viewed as living in a geometry in which space and time coordinates do not commute. (author)
Anomalies, Weinberg angle and a noncommutative geometric description of the standard model

International Nuclear Information System (INIS)

Scheck, F.

1992-01-01

The conditions on weak hypercharge assignments of quarks and leptons that are imposed by the absence of chiral anomalies, are identical with the supertrace conditions that appear in descriptions of the minimal standard model based on noncommutative geometry. Even though in these approaches there is no more explicit symmetry in the electroweak sector than the well-known SU(2) L xU(1), the noncommutative, graded algebra characterized by the modified exterior (Cartan and discrete) derivative is stringent enough to fix - at the classical level - the Weinberg angle. With the usual fermion content of the standard model the value typical for grand unified theories is found. (orig.)

Testing Non-commutative QED, Constructing Non-commutative MHD

OpenAIRE

Guralnik, Z.; Jackiw, R.; Pi, S. Y.; Polychronakos, A. P.

2001-01-01

The effect of non-commutativity on electromagnetic waves violates Lorentz invariance: in the presence of a background magnetic induction field b, the velocity for propagation transverse to b differs from c, while propagation along b is unchanged. In principle, this allows a test by the Michelson-Morley interference method. We also study non-commutativity in another context, by constructing the theory describing a charged fluid in a strong magnetic field, which forces the fluid particles into ...
Space-time philosophy reconstructed via massive Nordström scalar gravities? Laws vs. geometry, conventionality, and underdetermination

Science.gov (United States)

Pitts, J. Brian

2016-02-01

What if gravity satisfied the Klein-Gordon equation? Both particle physics from the 1920-30s and the 1890s Neumann-Seeliger modification of Newtonian gravity with exponential decay suggest considering a "graviton mass term" for gravity, which is algebraic in the potential. Unlike Nordström's "massless" theory, massive scalar gravity is strictly special relativistic in the sense of being invariant under the Poincaré group but not the 15-parameter Bateman-Cunningham conformal group. It therefore exhibits the whole of Minkowski space-time structure, albeit only indirectly concerning volumes. Massive scalar gravity is plausible in terms of relativistic field theory, while violating most interesting versions of Einstein's principles of general covariance, general relativity, equivalence, and Mach. Geometry is a poor guide to understanding massive scalar gravity(s): matter sees a conformally flat metric due to universal coupling, but gravity also sees the rest of the flat metric (barely or on long distances) in the mass term. What is the 'true' geometry, one might wonder, in line with Poincaré's modal conventionality argument? Infinitely many theories exhibit this bimetric 'geometry,' all with the total stress-energy's trace as source; thus geometry does not explain the field equations. The irrelevance of the Ehlers-Pirani-Schild construction to a critique of conventionalism becomes evident when multi-geometry theories are contemplated. Much as Seeliger envisaged, the smooth massless limit indicates underdetermination of theories by data between massless and massive scalar gravities-indeed an unconceived alternative. At least one version easily could have been developed before General Relativity; it then would have motivated thinking of Einstein's equations along the lines of Einstein's newly re-appreciated "physical strategy" and particle physics and would have suggested a rivalry from massive spin 2 variants of General Relativity (massless spin 2, Pauli and Fierz
Phenomenology of noncommutative field theories

International Nuclear Information System (INIS)

Carone, C D

2006-01-01

Experimental limits on the violation of four-dimensional Lorentz invariance imply that noncommutativity among ordinary spacetime dimensions must be small. In this talk, I review the most stringent bounds on noncommutative field theories and suggest a possible means of evading them: noncommutativity may be restricted to extra, compactified spatial dimensions. Such theories have a number of interesting features, including Abelian gauge fields whose Kaluza-Klein excitations have self couplings. We consider six-dimensional QED in a noncommutative bulk, and discuss the collider signatures of the model
Classical mechanics in non-commutative phase space

International Nuclear Information System (INIS)

Wei Gaofeng; Long Chaoyun; Long Zhengwen; Qin Shuijie

2008-01-01

In this paper the laws of motion of classical particles have been investigated in a non-commutative phase space. The corresponding non-commutative relations contain not only spatial non-commutativity but also momentum non-commutativity. First, new Poisson brackets have been defined in non-commutative phase space. They contain corrections due to the non-commutativity of coordinates and momenta. On the basis of this new Poisson brackets, a new modified second law of Newton has been obtained. For two cases, the free particle and the harmonic oscillator, the equations of motion are derived on basis of the modified second law of Newton and the linear transformation (Phys. Rev. D, 2005, 72: 025010). The consistency between both methods is demonstrated. It is shown that a free particle in commutative space is not a free particle with zero-acceleration in the non-commutative phase space, but it remains a free particle with zero-acceleration in non-commutative space if only the coordinates are non-commutative. (authors)
(Non-)commutative closed string on T-dual toroidal backgrounds

CERN Document Server

Andriot, David; Lust, Dieter; Patalong, Peter

2013-01-01

In this paper we investigate the connection between (non-)geometry and (non-)commutativity of the closed string. To this end, we solve the classical string on three T-dual toroidal backgrounds: a torus with H-flux, a twisted torus and a non-geometric background with Q-flux. In all three situations we work under the assumption of a dilute flux and consider quantities to linear order in the flux density. Furthermore, we perform the first steps of a canonical quantization for the twisted torus, to derive commutators of the string expansion modes. We use them as well as T-duality to determine, in the non-geometric background, a commutator of two string coordinates, which turns out to be non-vanishing. We relate this non-commutativity to the closed string boundary conditions, and the non-geometric Q-flux.
Noncommutative Valuation of Options

Science.gov (United States)

Herscovich, Estanislao

2016-12-01

The aim of this note is to show that the classical results in finance theory for pricing of derivatives, given by making use of the replication principle, can be extended to the noncommutative world. We believe that this could be of interest in quantum probability. The main result called the First fundamental theorem of asset pricing, states that a noncommutative stock market admits no-arbitrage if and only if it admits a noncommutative equivalent martingale probability.
Non-commutative algebra of functions of 4-dimensional quantum Hall droplet

International Nuclear Information System (INIS)

Chen Yixin; Hou Boyu; Hou Boyuan

2002-01-01

We develop the description of non-commutative geometry of the 4-dimensional quantum Hall fluid's theory proposed recently by Zhang and Hu. The non-commutative structure of fuzzy S 4 , which is the base of the bundle S 7 obtained by the second Hopf fibration, i.e., S 7 /S 3 =S 4 , appears naturally in this theory. The fuzzy monopole harmonics, which are the essential elements in the non-commutative algebra of functions on S 4 , are explicitly constructed and their obeying the matrix algebra is obtained. This matrix algebra is associative. We also propose a fusion scheme of the fuzzy monopole harmonics of the coupling system from those of the subsystems, and determine the fusion rule in such fusion scheme. By products, we provide some essential ingredients of the theory of SO(5) angular momentum. In particular, the explicit expression of the coupling coefficients, in the theory of SO(5) angular momentum, are given. We also discuss some possible applications of our results to the 4-dimensional quantum Hall system and the matrix brane construction in M-theory
Noncommutative calculi of probabilty

Directory of Open Access Journals (Sweden)

Michał Heller

2010-12-01

Full Text Available The paper can be regarded as a short and informal introduction to noncommutative calculi of probability. The standard theory of probability is reformulated in the algebraic language. In this form it is readily generalized to that its version which is virtually present in quantum mechanics, and then generalized to the so-called free theory of probability. Noncommutative theory of probability is a pair (M, φ where M is a von Neumann algebra, and φ a normal state on M which plays the role of a noncommutative probability measure. In the standard (commutative theory of probability, there is, in principle, one mathematically interesting probability measure, namely the Lebesgue measure, whereas in the noncommutative theories there are many nonequivalent probability measures. Philosophical implications of this fact are briefly discussed.
Hall effect in noncommutative coordinates

International Nuclear Information System (INIS)

Dayi, Oemer F.; Jellal, Ahmed

2002-01-01

We consider electrons in uniform external magnetic and electric fields which move on a plane whose coordinates are noncommuting. Spectrum and eigenfunctions of the related Hamiltonian are obtained. We derive the electric current whose expectation value gives the Hall effect in terms of an effective magnetic field. We present a receipt to find the action which can be utilized in path integrals for noncommuting coordinates. In terms of this action we calculate the related Aharonov-Bohm phase and show that it also yields the same effective magnetic field. When magnetic field is strong enough this phase becomes independent of magnetic field. Measurement of it may give some hints on spatial noncommutativity. The noncommutativity parameter θ can be tuned such that electrons moving in noncommutative coordinates are interpreted as either leading to the fractional quantum Hall effect or composite fermions in the usual coordinates
Noncommutative quantum field theory: attempts on renormalization

International Nuclear Information System (INIS)

Popp, L.

2002-05-01

Quantum field theory is the art of dealing with problems at small distances or, equivalently, large momenta. Although there are different approaches (string theory, for example), it is generally accepted that these principles cannot be extrapolated to arbitrarily small distances as can be shown by applying simple, heuristic arguments. Therefore, the concept of space-time as a differential manifold has to be replaced by something else at such scales, the road we have chosen to follow is noncommutative geometry. We start from the basic relation [ x μ , x ν ] = i θ { μν}, where θ is a (usually) constant, antisymmetric matrix. This relation amounts to a noncommutativity of position measurements, or, put differently, the points are somehow 'smeared' out, which should have a positive effect on field theory since infinities arise from point-like interactions. However, it was shown that the effects of the commutation relation (leading to the so-called Moyal product) do not necessarily cure the divergences but introduce a new kind of problem: whereas UV-divergent integrals are rendered finite by phase factors (that arise as a consequence of the Moyal product), this same kind of 'regularization' introduces IR-divergences which led to the name 'UV/IR-mixing' for this problem. In order to overcome this peculiarity, one expands the action in θ which is immediate for the phase factors but requires the so-called Seiberg-Witten map for the fields. In this thesis, we emphasize the derivation of the Seiberg-Witten map by using noncommutative Lorentz symmetries, which is more general than the original derivation. After that, we concentrate on a treatment of θ-expanded theories and their renormalization, where it can be shown that the photon self-energy of noncommutative Maxwell theory can be renormalized to all orders in hbar and θ when the freedom in the Seiberg-Witten map (there are ambiguities in the map) is exploited. Although this is very promising, it cannot be
Noncommutative QED and anomalous dipole moments

International Nuclear Information System (INIS)

Riad, I.F.; Sheikh-Jabbari, M.M.

2000-09-01

We study QED on noncommutative spaces, NCQED. In particular we present the detailed calculation for the noncommutative electron-photon vertex and show that the Ward identity is satisfied. We discuss that in the noncommutative case moving electron will show electric dipole effects. In addition, we work out the electric and magnetic dipole moments up to one loop level. For the magnetic moment we show that noncommutative electron has an intrinsic (spin independent) magnetic moment. (author)
Space-Time Diffeomorphisms in Noncommutative Gauge Theories

Directory of Open Access Journals (Sweden)

L. Román Juarez

2008-07-01

Full Text Available In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007, 10367–10382] we have shown how for canonical parametrized field theories, where space-time is placed on the same footing as the other fields in the theory, the representation of space-time diffeomorphisms provides a very convenient scheme for analyzing the induced twisted deformation of these diffeomorphisms, as a result of the space-time noncommutativity. However, for gauge field theories (and of course also for canonical geometrodynamics where the Poisson brackets of the constraints explicitely depend on the embedding variables, this Poisson algebra cannot be connected directly with a representation of the complete Lie algebra of space-time diffeomorphisms, because not all the field variables turn out to have a dynamical character [Isham C.J., Kuchar K.V., Ann. Physics 164 (1985, 288–315, 316–333]. Nonetheless, such an homomorphic mapping can be recuperated by first modifying the original action and then adding additional constraints in the formalism in order to retrieve the original theory, as shown by Kuchar and Stone for the case of the parametrized Maxwell field in [Kuchar K.V., Stone S.L., Classical Quantum Gravity 4 (1987, 319–328]. Making use of a combination of all of these ideas, we are therefore able to apply our canonical reparametrization approach in order to derive the deformed Lie algebra of the noncommutative space-time diffeomorphisms as well as to consider how gauge transformations act on the twisted algebras of gauge and particle fields. Thus, hopefully, adding clarification on some outstanding issues in the literature concerning the symmetries for gauge theories in noncommutative space-times.
D1/D5 system with B-field, noncommutative geometry and the CFT of the higgs branch

CERN Document Server

Dhar, A; Wadia, S R; Yogendran, K P; Dhar, Avinash; Mandal, Gautam; Wadia, Spenta R.

2000-01-01

The D1/D5 system is considered in the presence of the NS B field. An explicit supergravity solution in the asymptotically flat and near horizon limits is presented. Explicit mass formulae are presented in both cases. This solution has no D3 source branes and represents a true bound state of the D1/D5 system. We study the motion of a separated D1-brane in the background geometry described above and reproduce the Liouville potential that binds the D1 brane. A gauge theory analysis is also presented in the presence of Fayet-Iliopoulos (FI) parameters which can be identified with the self-dual part of the NS B field. In the case of a single D5-brane and an arbitrary number of D1 branes we can demonstrate the existence of a bound state in the Higgs branch. We also point out the connection of the SCFT on the resolved Sym$_{Q_1Q_5}(\\tilde T^4)$ with recent developments in non-commutative Yang-Mills theory.
Noncommutative products of Euclidean spaces

Science.gov (United States)

Dubois-Violette, Michel; Landi, Giovanni

2018-05-01

We present natural families of coordinate algebras on noncommutative products of Euclidean spaces R^{N_1} × _R R^{N_2} . These coordinate algebras are quadratic ones associated with an R -matrix which is involutive and satisfies the Yang-Baxter equations. As a consequence, they enjoy a list of nice properties, being regular of finite global dimension. Notably, we have eight-dimensional noncommutative euclidean spaces R4 × _R R4 . Among these, particularly well behaved ones have deformation parameter u \\in S^2 . Quotients include seven spheres S7_u as well as noncommutative quaternionic tori TH_u = S^3 × _u S^3 . There is invariance for an action of {{SU}}(2) × {{SU}}(2) on the torus TH_u in parallel with the action of U(1) × U(1) on a `complex' noncommutative torus T^2_θ which allows one to construct quaternionic toric noncommutative manifolds. Additional classes of solutions are disjoint from the classical case.
Noncommutative CPN and CHN and their physics

International Nuclear Information System (INIS)

Sako, Akifumi; Suzuki, Toshiya; Umetsu, Hiroshi

2013-01-01

We study noncommutative deformation of manifolds by constructing star products. We start from a noncommutative R d and discuss more genaral noncommutative manifolds. In general, star products can not be described in concrete expressions without some exceptions. In this article we introduce new examples of noncommutative manifolds with explicit star products. Karabegov's deformation quantization of CP N and CH N with separation of variables gives explicit calulable star products represented by gamma functions. Using the results of star products between inhomogeneous coordinates, we find creation and anihilation operators and obtain the Fock representation of the noncommutative CP N and CH N .
From Quantum Deformations of Relativistic Symmetries to Modified Kinematics and Dynamics

International Nuclear Information System (INIS)

Lukierski, J.

2010-01-01

We present a short review describing the use of noncommutative spacetime in quantum-deformed dynamical theories: classical and quantum mechanics as well as classical and quantum field theory. We expose the role of Hopf algebras and their realizations (noncommutative modules) as important mathematical tool describing quantum-deformed symmetries: quantum Lie groups and quantum Lie algebras. We consider in some detail the most studied examples of noncommutative space-time geometry: the canonical and κ-deformed cases. Finally, we briefly describe the modifications of Einstein gravity obtained by introduction of noncommutative space-time coordinates. (author)
Non-commutative standard model: model building

CERN Document Server

Chaichian, Masud; Presnajder, P

2003-01-01

A non-commutative version of the usual electro-weak theory is constructed. We discuss how to overcome the two major problems: (1) although we can have non-commutative U(n) (which we denote by U sub * (n)) gauge theory we cannot have non-commutative SU(n) and (2) the charges in non-commutative QED are quantized to just 0,+-1. We show how the latter problem with charge quantization, as well as with the gauge group, can be resolved by taking the U sub * (3) x U sub * (2) x U sub * (1) gauge group and reducing the extra U(1) factors in an appropriate way. Then we proceed with building the non-commutative version of the standard model by specifying the proper representations for the entire particle content of the theory, the gauge bosons, the fermions and Higgs. We also present the full action for the non-commutative standard model (NCSM). In addition, among several peculiar features of our model, we address the inherentCP violation and new neutrino interactions. (orig.)
Noncommutative Blackwell-Ross martingale inequality

Science.gov (United States)

Talebi, Ali; Moslehian, Mohammad Sal; Sadeghi, Ghadir

We establish a noncommutative Blackwell-Ross inequality for supermartingales under a suitable condition which generalizes Khan’s work to the noncommutative setting. We then employ it to deduce an Azuma-type inequality.
Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action

Energy Technology Data Exchange (ETDEWEB)

Gitman, D.M. [Universidade de Sao Paulo, Instituto de Fisica, Sao Paulo, SP (Brazil); Kupriyanov, V.G. [Universidade de Sao Paulo, Instituto de Fisica, Sao Paulo, SP (Brazil); Tomsk State University, Physics Department, Tomsk (Russian Federation)

2008-03-15

It is known that the actions of field theories on a noncommutative space-time can be written as some modified (we call them {theta}-modified) classical actions already on the commutative space-time (introducing a star product). Then the quantization of such modified actions reproduces both space-time noncommutativity and the usual quantum mechanical features of the corresponding field theory. In the present article, we discuss the problem of constructing {theta}-modified actions for relativistic QM. We construct such actions for relativistic spinless and spinning particles. The key idea is to extract {theta}-modified actions of the relativistic particles from path-integral representations of the corresponding noncommutative field theory propagators. We consider the Klein-Gordon and Dirac equations for the causal propagators in such theories. Then we construct for the propagators path-integral representations. Effective actions in such representations we treat as {theta}-modified actions of the relativistic particles. To confirm the interpretation, we canonically quantize these actions. Thus, we obtain the Klein-Gordon and Dirac equations in the noncommutative field theories. The {theta}-modified action of the relativistic spinning particle is just a generalization of the Berezin-Marinov pseudoclassical action for the noncommutative case. (orig.)
Non-commutative tools for topological insulators

International Nuclear Information System (INIS)

Prodan, Emil

2010-01-01

This paper reviews several analytic tools for the field of topological insulators, developed with the aid of non-commutative calculus and geometry. The set of tools includes bulk topological invariants defined directly in the thermodynamic limit and in the presence of disorder, whose robustness is shown to have nontrivial physical consequences for the bulk states. The set of tools also includes a general relation between the current of an observable and its edge index, a relation that can be used to investigate the robustness of the edge states against disorder. The paper focuses on the motivations behind creating such tools and on how to use them.

Noncommutative time in quantum field theory

International Nuclear Information System (INIS)

Salminen, Tapio; Tureanu, Anca

2011-01-01

We analyze, starting from first principles, the quantization of field theories, in order to find out to which problems a noncommutative time would possibly lead. We examine the problem in the interaction picture (Tomonaga-Schwinger equation), the Heisenberg picture (Yang-Feldman-Kaellen equation), and the path integral approach. They all indicate inconsistency when time is taken as a noncommutative coordinate. The causality issue appears as the key aspect, while the unitarity problem is subsidiary. These results are consistent with string theory, which does not admit a time-space noncommutative quantum field theory as its low-energy limit, with the exception of lightlike noncommutativity.
Can Topology and Geometry be Measured by an Operator Measurement in Quantum Gravity?

Science.gov (United States)

Berenstein, David; Miller, Alexandra

2017-06-30

In the context of Lin-Lunin-Maldacena geometries, we show that superpositions of classical coherent states of trivial topology can give rise to new classical limits where the topology of spacetime has changed. We argue that this phenomenon implies that neither the topology nor the geometry of spacetime can be the result of an operator measurement. We address how to reconcile these statements with the usual semiclassical analysis of low energy effective field theory for gravity.
Covariant Renormalizable Modified and Massive Gravity Theories on (Non) Commutative Tangent Lorentz Bundles

CERN Document Server

Vacaru, Sergiu I

2014-01-01

The fundamental field equations in modified gravity (including general relativity; massive and bimetric theories; Ho\\vrava-Lifshits, HL; Einstein--Finsler gravity extensions etc) posses an important decoupling property with respect to nonholonomic frames with 2 (or 3) +2+2+... spacetime decompositions. This allows us to construct exact solutions with generic off--diagonal metrics depending on all spacetime coordinates via generating and integration functions containing (un-) broken symmetry parameters. Such nonholonomic configurations/ models have a nice ultraviolet behavior and seem to be ghost free and (super) renormalizable in a sense of covariant and/or massive modifications of HL gravity. The apparent noncommutativity and breaking of Lorentz invariance by quantum effects can be encoded into fibers of noncommutative tangent Lorentz bundles for corresponding "partner" anisotropically induced theories. We show how the constructions can be extended to include conjectured covariant reonormalizable models with...
Noncommutative instantons via dressing and splitting approaches

International Nuclear Information System (INIS)

Horvath, Zalan; Lechtenfeld, Olaf; Wolf, Martin

2002-01-01

Almost all known instanton solutions in noncommutative Yang-Mills theory have been obtained in the modified ADHM scheme. In this paper we employ two alternative methods for the construction of the self-dual U(2) BPST instanton on a noncommutative euclidean four-dimensional space with self-dual noncommutativity tensor. Firstly, we use the method of dressing transformations, an iterative procedure for generating solutions from a given seed solution, and thereby generalize Belavin's and Zakharov's work to the noncommutative setup. Secondly, we relate the dressing approach with Ward's splitting method based on the twistor construction and rederive the solution in this context. It seems feasible to produce nonsingular noncommutative multi-instantons with these techniques. (author)
Covariant non-commutative space–time

Directory of Open Access Journals (Sweden)

Jonathan J. Heckman

2015-05-01

Full Text Available We introduce a covariant non-commutative deformation of 3+1-dimensional conformal field theory. The deformation introduces a short-distance scale ℓp, and thus breaks scale invariance, but preserves all space–time isometries. The non-commutative algebra is defined on space–times with non-zero constant curvature, i.e. dS4 or AdS4. The construction makes essential use of the representation of CFT tensor operators as polynomials in an auxiliary polarization tensor. The polarization tensor takes active part in the non-commutative algebra, which for dS4 takes the form of so(5,1, while for AdS4 it assembles into so(4,2. The structure of the non-commutative correlation functions hints that the deformed theory contains gravitational interactions and a Regge-like trajectory of higher spin excitations.
Spin Hall effect on a noncommutative space

International Nuclear Information System (INIS)

Ma Kai; Dulat, Sayipjamal

2011-01-01

We study the spin-orbital interaction and the spin Hall effect of an electron moving on a noncommutative space under the influence of a vector potential A(vector sign). On a noncommutative space, we find that the commutator between the vector potential A(vector sign) and the electric potential V 1 (r(vector sign)) of the lattice induces a new term, which can be treated as an effective electric field, and the spin Hall conductivity obtains some correction. On a noncommutative space, the spin current and spin Hall conductivity have distinct values in different directions, and depend explicitly on the noncommutative parameter. Once this spin Hall conductivity in different directions can be measured experimentally with a high level of accuracy, the data can then be used to impose bounds on the value of the space noncommutativity parameter. We have also defined a new parameter, σ=ρθ (ρ is the electron concentration, θ is the noncommutativity parameter), which can be measured experimentally. Our approach is based on the Foldy-Wouthuysen transformation, which gives a general Hamiltonian of a nonrelativistic electron moving on a noncommutative space.
Non commutative geometry and super Yang-Mills theory

International Nuclear Information System (INIS)

Bigatti, D.

1999-01-01

We aim to connect the non commutative geometry 'quotient space' viewpoint with the standard super Yang Mills theory approach in the spirit of Connes-Douglas-Schwartz and Douglas-Hull description of application of noncommutative geometry to matrix theory. This will result in a relation between the parameters of a rational foliation of the torus and the dimension of the group U(N). Namely, we will be provided with a prescription which allows to study a noncommutative geometry with rational parameter p/N by means of a U(N) gauge theory on a torus of size Σ/N with the boundary conditions given by a system with p units of magnetic flux. The transition to irrational parameter can be obtained by letting N and p tend to infinity with fixed ratio. The precise meaning of the limiting process will presumably allow better clarification. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)
Noncommutative gauge field theories: A no-go theorem

International Nuclear Information System (INIS)

Chaichian, M.; Tureanu, A.; Presnajder, P.; Sheikh-Jabbari, M.M.

2001-06-01

Studying the mathematical structure of the noncommutative groups in more detail, we prove a no-go theorem for the noncommutative gauge theories. According to this theorem, the closure condition of the gauge algebra implies that: 1) the local noncommutative u(n) algebra only admits the irreducible nxn matrix-representation. Hence the gauge fields, as elements of the algebra, are in nxn matrix form, while the matter fields can only be either in fundamental, adjoint or singlet states; 2) for any gauge group consisting of several simple group factors, the matter fields can transform nontrivially under at most two noncommutative group factors. In other words, the matter fields cannot carry more than two simple noncommutative gauge group charges. This no-go theorem imposes strong restrictions on the construction of the noncommutative version of the Standard Model and in resolving the standing problem of charge quantization in noncommutative QED. (author)
Noncommutative solitons

International Nuclear Information System (INIS)

Gopakumar, R.

2002-01-01

Though noncommutative field theories have been explored for several years, a resurgence of interest in it was sparked off after it was realised that they arise very naturally as limits of string theory in certain background fields. It became more plausible (at least to string theorists) that these nonlocal deformations of usual quantum field theories are consistent theories in themselves. This led to a detailed exploration of many of their classical and quantum properties. I will elaborate further on the string theory context in the next section. One of the consequences of this exploration was the discovery of novel classical solutions in noncommutative field theories. Since then much work has been done in exploring many of their novel properties. My lectures focussed on some specific aspects of these noncommutative solitons. They primarily reflect the topics that I have worked on and are not intended to be a survey of the large amount of work on this topic. We have tried to give a flavour of the physics that can be captured by the relatively elementary classical solutions of noncommutative field theories. We have seen in different contexts how these solitons are really simple manifestations of D-branes, possessing many of their important features. Though they have been primarily studied in the context of tachyon condensation, we saw that they can also shed some light on the resolution of singularities in spacetime by D-brane probes. In addition to other applications in string theory it is important at this stage to explore their presence in other systems with a strong magnetic field like the quantum hall effect
Noncommutative solitons

Energy Technology Data Exchange (ETDEWEB)

Gopakumar, R [Harish-Chandra Research Institute, Jhusi, Allahabad (India)

2002-05-15

Though noncommutative field theories have been explored for several years, a resurgence of interest in it was sparked off after it was realised that they arise very naturally as limits of string theory in certain background fields. It became more plausible (at least to string theorists) that these nonlocal deformations of usual quantum field theories are consistent theories in themselves. This led to a detailed exploration of many of their classical and quantum properties. I will elaborate further on the string theory context in the next section. One of the consequences of this exploration was the discovery of novel classical solutions in noncommutative field theories. Since then much work has been done in exploring many of their novel properties. My lectures focussed on some specific aspects of these noncommutative solitons. They primarily reflect the topics that I have worked on and are not intended to be a survey of the large amount of work on this topic. We have tried to give a flavour of the physics that can be captured by the relatively elementary classical solutions of noncommutative field theories. We have seen in different contexts how these solitons are really simple manifestations of D-branes, possessing many of their important features. Though they have been primarily studied in the context of tachyon condensation, we saw that they can also shed some light on the resolution of singularities in spacetime by D-brane probes. In addition to other applications in string theory it is important at this stage to explore their presence in other systems with a strong magnetic field like the quantum hall effect.
Noncommutativity and unitarity violation in gauge boson scattering

International Nuclear Information System (INIS)

Hewett, J. L.; Petriello, F. J.; Rizzo, T. G.

2002-01-01

We examine the unitarity properties of spontaneously broken noncommutative gauge theories. We find that the symmetry breaking mechanism in the noncommutative standard model of Chaichian et al. leads to an unavoidable violation of tree-level unitarity in gauge boson scattering at high energies. We then study a variety of simplified spontaneously broken noncommutative theories and isolate the source of this unitarity violation. Given the group theoretic restrictions endemic to noncommutative model building, we conclude that it is difficult to build a noncommutative standard model under the Weyl-Moyal approach that preserves unitarity
Exact multi-line soliton solutions of noncommutative KP equation

International Nuclear Information System (INIS)

Wang, Ning; Wadati, Miki

2003-01-01

A method of solving noncommutative linear algebraic equations plays a key role in the extension of the ∂-bar -dressing on the noncommutative space-time manifold. In this paper, a solution-generating method of noncommutative linear algebraic equations is proposed. By use of the proposed method, a class of multi-line soliton solutions of noncommutative KP (ncKP) equation is constructed explicitly. The method is expected to be of use for constructions of noncommutative soliton equations. The significance of the noncommutativity of coordinates is investigated. It is found that the noncommutativity of the space-time coordinate has a role to split the spatial waveform of the classical multi-line solitons and reform it to a new configuration. (author)
Workshop on Non-Associative & Non-Commutative Algebra and Operator Theory

CERN Document Server

Molina, Mercedes

2016-01-01

Presenting the collaborations of over thirty international experts in the latest developments in pure and applied mathematics, this volume serves as an anthology of research with a common basis in algebra, functional analysis and their applications. Special attention is devoted to non-commutative algebras, non-associative algebras, operator theory and ring and module theory. These themes are relevant in research and development in coding theory, cryptography and quantum mechanics. The topics in this volume were presented at the Workshop on Non-Associative & Non-Commutative Algebra and Operator Theory, held May 23—25, 2014 at Cheikh Anta Diop University in Dakar, Senegal in honor of Professor Amin Kaidi. The workshop was hosted by the university's Laboratory of Algebra, Cryptology, Algebraic Geometry and Applications, in cooperation with the University of Almería and the University of Málaga. Dr. Kaidi's work focuses on non-associative rings and algebras, operator theory and functional analysis, and he...
A Immirzi-like parameter for 3D quantum gravity

International Nuclear Information System (INIS)

Bonzom, Valentin; Livine, Etera R

2008-01-01

We study an Immirzi-like ambiguity in three-dimensional quantum gravity. It shares some features with the Immirzi parameter of four-dimensional loop quantum gravity: it does not affect the equations of motion, but modifies the Poisson brackets and the constraint algebra at the canonical level. We focus on the length operator and show how to define it through non-commuting fluxes. We compute its spectrum and show the effect of this Immirzi-like ambiguity. Finally, we extend these considerations to 4D gravity and show how the different topological modifications of the action affect the canonical structure of loop quantum gravity
Canonical noncommutativity in special and general relativity

Energy Technology Data Exchange (ETDEWEB)

Chryssomalakos, C; Hernandez, H; Okon, E; Vazquez Montejo, P [Instituto de Ciencias Nucleares, Universidad National Autonoma de Mexico, 04510 Mexico, D.F. (Mexico)

2007-05-15

There are two main points that concern us in this short contribution. The first one is the conceptual distinction between a intrinsically noncommuting spacetime, i.e., one where the coordinate functions fail to commute among themselves, on the one hand, and the proposal of noncommuting position operators, on the other. The second point concerns a particular form of position operator noncommutativity, involving the spin of the particle, to which several approaches seem to converge. We also suggest an analysis of the effects of spacetime curvature on position operator noncommutativity.
Noncommutative quantum electrodynamics in path integral framework

International Nuclear Information System (INIS)

Bourouaine, S; Benslama, A

2005-01-01

In this paper, the dynamics of a relativistic particle of spin 1/2, interacting with an external electromagnetic field in noncommutative space, is studied in the path integral framework. By adopting the Fradkin-Gitman formulation, the exact Green's function in noncommutative space (NCGF) for the quadratic case of a constant electromagnetic field is computed, and it is shown that its form is similar to its counterpart given in commutative space. In addition, it is deduced that the effect of noncommutativity has the same effect as an additional constant field depending on a noncommutative θ matrix
Noncommutative analysis, operator theory and applications

CERN Document Server

Cipriani, Fabio; Colombo, Fabrizio; Guido, Daniele; Sabadini, Irene; Sauvageot, Jean-Luc

2016-01-01

This book illustrates several aspects of the current research activity in operator theory, operator algebras and applications in various areas of mathematics and mathematical physics. It is addressed to specialists but also to graduate students in several fields including global analysis, Schur analysis, complex analysis, C*-algebras, noncommutative geometry, operator algebras, operator theory and their applications. Contributors: F. Arici, S. Bernstein, V. Bolotnikov, J. Bourgain, P. Cerejeiras, F. Cipriani, F. Colombo, F. D'Andrea, G. Dell'Antonio, M. Elin, U. Franz, D. Guido, T. Isola, A. Kula, L.E. Labuschagne, G. Landi, W.A. Majewski, I. Sabadini, J.-L. Sauvageot, D. Shoikhet, A. Skalski, H. de Snoo, D. C. Struppa, N. Vieira, D.V. Voiculescu, and H. Woracek.
Spinning geometry = Twisted geometry

International Nuclear Information System (INIS)

Freidel, Laurent; Ziprick, Jonathan

2014-01-01

It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries are not continuous across the faces. Here we show that this phase space can also be represented by continuous, piecewise-flat three-geometries called spinning geometries. These are composed of metric-flat three-cells glued together consistently. The geometry of each cell and the manner in which they are glued is compatible with the choice of fluxes and holonomies. We first remark that the fluxes provide each edge with an angular momentum. By studying the piecewise-flat geometries which minimize edge lengths, we show that these angular momenta can be literally interpreted as the spin of the edges: the geometries of all edges are necessarily helices. We also show that the compatibility of the gluing maps with the holonomy data results in the same conclusion. This shows that a spinning geometry represents a way to glue together the three-cells of a twisted geometry to form a continuous geometry which represents a point in the loop gravity phase space. (paper)
Noncommuting fields and non-Abelian fluids

International Nuclear Information System (INIS)

Jackiw, R.

2004-01-01

The original ideas about noncommuting coordinates are recalled. The connection between U(1) gauge fields defined on noncommuting coordinates and fluid mechanics is explained. Non-Abelian fluid mechanics is described
Constraining the noncommutative spectral action via astrophysical observations.

Science.gov (United States)

Nelson, William; Ochoa, Joseph; Sakellariadou, Mairi

2010-09-03

The noncommutative spectral action extends our familiar notion of commutative spaces, using the data encoded in a spectral triple on an almost commutative space. Varying a rather simple action, one can derive all of the standard model of particle physics in this setting, in addition to a modified version of Einstein-Hilbert gravity. In this Letter we use observations of pulsar timings, assuming that no deviation from general relativity has been observed, to constrain the gravitational sector of this theory. While the bounds on the coupling constants remain rather weak, they are comparable to existing bounds on deviations from general relativity in other settings and are likely to be further constrained by future observations.

Unitary quantum physics with time-space non-commutativity

International Nuclear Information System (INIS)

Balachandran, A P; Govindarajan, T R; Martins, A G; Molina, C; Teotonio-Sobrinho, P

2005-01-01

In these lectures 4 quantum physics in noncommutative spacetime is developed. It is based on the work of Doplicher et al. which allows for time-space noncommutativity. In the context of noncommutative quantum mechanics, some important points are explored, such as the formal construction of the theory, symmetries, causality, simultaneity and observables. The dynamics generated by a noncommutative Schroedinger equation is studied. The theory is further extended to certain noncommutative versions of the cylinder, R 3 and R x S 3 . In all these models, only discrete time translations are possible. One striking consequence of quantised time translations is that even though a time independent Hamiltonian is an observable, in scattering processes, it is conserved only modulo 2π/θ, where θ is the noncommutative parameter. Scattering theory is formulated and an approach to quantumfield theory is outlined
Cardy-Verlinde Formula of Noncommutative Schwarzschild Black Hole

Directory of Open Access Journals (Sweden)

G. Abbas

2014-01-01

Full Text Available Few years ago, Setare (2006 has investigated the Cardy-Verlinde formula of noncommutative black hole obtained by noncommutativity of coordinates. In this paper, we apply the same procedure to a noncommutative black hole obtained by the coordinate coherent approach. The Cardy-Verlinde formula is entropy formula of conformal field theory in an arbitrary dimension. It relates the entropy of conformal field theory to its total energy and Casimir energy. In this paper, we have calculated the total energy and Casimir energy of noncommutative Schwarzschild black hole and have shown that entropy of noncommutative Schwarzschild black hole horizon can be expressed in terms of Cardy-Verlinde formula.
Noncommutative quantum electrodynamics in path integral framework

Energy Technology Data Exchange (ETDEWEB)

Bourouaine, S; Benslama, A [Departement de Physique, Faculte des Sciences, Universite Mentouri, Constantine (Algeria)

2005-08-19

In this paper, the dynamics of a relativistic particle of spin 1/2, interacting with an external electromagnetic field in noncommutative space, is studied in the path integral framework. By adopting the Fradkin-Gitman formulation, the exact Green's function in noncommutative space (NCGF) for the quadratic case of a constant electromagnetic field is computed, and it is shown that its form is similar to its counterpart given in commutative space. In addition, it is deduced that the effect of noncommutativity has the same effect as an additional constant field depending on a noncommutative {theta} matrix.
Supersymmetry on the noncommutative lattice

International Nuclear Information System (INIS)

Nishimura, Jun; Rey, Soo-Jong; Sugino, Fumihiko

2003-01-01

Built upon the proposal of Kaplan et al. (heplat{0206109}), we construct noncommutative lattice gauge theory with manifest supersymmetry. We show that such theory is naturally implementable via orbifold conditions generalizing those used by Kaplan et al. We present the prescription in detail and illustrate it for noncommutative gauge theories latticized partially in two dimensions. We point out a deformation freedom in the defining theory by a complex-parameter, reminiscent of discrete torsion in string theory. We show that, in the continuum limit, the supersymmetry is enhanced only at a particular value of the deformation parameter, determined solely by the size of the noncommutativity. (author)
Quantum symplectic geometry. 1. The matrix Hamiltonian formalism

International Nuclear Information System (INIS)

Djemai, A.E.F.

1994-07-01

The main purpose of this work is to describe the quantum analogue of the usual classical symplectic geometry and then to formulate the quantum mechanics as a (quantum) non-commutative symplectic geometry. In this first part, we define the quantum symplectic structure in the context of the matrix differential geometry by using the discrete Weyl-Schwinger realization of the Heisenberg group. We also discuss the continuous limit and give an expression of the quantum structure constants. (author). 42 refs
Foundations of free noncommutative function theory

CERN Document Server

Kaliuzhnyi-Verbovetskyi, Dmitry S

2014-01-01

In this book the authors develop a theory of free noncommutative functions, in both algebraic and analytic settings. Such functions are defined as mappings from square matrices of all sizes over a module (in particular, a vector space) to square matrices over another module, which respect the size, direct sums, and similarities of matrices. Examples include, but are not limited to, noncommutative polynomials, power series, and rational expressions. Motivation and inspiration for using the theory of free noncommutative functions often comes from free probability. An important application area is "dimensionless" matrix inequalities; these arise, e.g., in various optimization problems of system engineering. Among other related areas are those of polynomial identities in rings, formal languages and finite automata, quasideterminants, noncommutative symmetric functions, operator spaces and operator algebras, and quantum control.
Emergent geometry of membranes

Energy Technology Data Exchange (ETDEWEB)

Badyn, Mathias Hudoba de; Karczmarek, Joanna L.; Sabella-Garnier, Philippe; Yeh, Ken Huai-Che [Department of Physics and Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver (Canada)

2015-11-13

In work http://dx.doi.org/10.1103/PhysRevD.86.086001, a surface embedded in flat ℝ{sup 3} is associated to any three hermitian matrices. We study this emergent surface when the matrices are large, by constructing coherent states corresponding to points in the emergent geometry. We find the original matrices determine not only shape of the emergent surface, but also a unique Poisson structure. We prove that commutators of matrix operators correspond to Poisson brackets. Through our construction, we can realize arbitrary noncommutative membranes: for example, we examine a round sphere with a non-spherically symmetric Poisson structure. We also give a natural construction for a noncommutative torus embedded in ℝ{sup 3}. Finally, we make remarks about area and find matrix equations for minimal area surfaces.
Some remarks on K_0 of noncommutative tori

OpenAIRE

Chakraborty, Sayan

2017-01-01

Using Rieffel's construction of projective modules over higher dimensional noncommutative tori, we construct projective modules over some continuous field of C*-algebras whose fibers are noncommutative tori. Using a result of Echterhoff et al., our construction gives generators of K_0 of all noncommutative tori.
The matter Lagrangian and the energy-momentum tensor in modified gravity with nonminimal coupling between matter and geometry

International Nuclear Information System (INIS)

Harko, T.

2010-01-01

We show that in modified f(R) type gravity models with nonminimal coupling between matter and geometry, both the matter Lagrangian and the energy-momentum tensor are completely and uniquely determined by the form of the coupling. This result is obtained by using the variational formulation for the derivation of the equations of motion in the modified gravity models with geometry-matter coupling, and the Newtonian limit for a fluid obeying a barotropic equation of state. The corresponding energy-momentum tensor of the matter in modified gravity models with nonminimal coupling is more general than the usual general-relativistic energy-momentum tensor for perfect fluids, and it contains a supplementary, equation of state dependent term, which could be related to the elastic stresses in the body, or to other forms of internal energy. Therefore, the extra force induced by the coupling between matter and geometry never vanishes as a consequence of the thermodynamic properties of the system, or for a specific choice of the matter Lagrangian, and it is nonzero in the case of a fluid of dust particles.
Noncommutative Geometry of the Moyal Plane: Translation Isometries, Connes' Distance on Coherent States, Pythagoras Equality

Science.gov (United States)

Martinetti, Pierre; Tomassini, Luca

2013-10-01

We study the metric aspect of the Moyal plane from Connes' noncommutative geometry point of view. First, we compute Connes' spectral distance associated with the natural isometric action of on the algebra of the Moyal plane . We show that the distance between any state of and any of its translated states is precisely the amplitude of the translation. As a consequence, we obtain the spectral distance between coherent states of the quantum harmonic oscillator as the Euclidean distance on the plane. We investigate the classical limit, showing that the set of coherent states equipped with Connes' spectral distance tends towards the Euclidean plane as the parameter of deformation goes to zero. The extension of these results to the action of the symplectic group is also discussed, with particular emphasis on the orbits of coherent states under rotations. Second, we compute the spectral distance in the double Moyal plane, intended as the product of (the minimal unitization of) by . We show that on the set of states obtained by translation of an arbitrary state of , this distance is given by the Pythagoras theorem. On the way, we prove some Pythagoras inequalities for the product of arbitrary unital and non-degenerate spectral triples. Applied to the Doplicher- Fredenhagen-Roberts model of quantum spacetime [DFR], these two theorems show that Connes' spectral distance and the DFR quantum length coincide on the set of states of optimal localization.
Trace Dynamics and a non-commutative special relativity

International Nuclear Information System (INIS)

Lochan, Kinjalk; Singh, T.P.

2011-01-01

Trace Dynamics is a classical dynamical theory of non-commuting matrices in which cyclic permutation inside a trace is used to define the derivative with respect to an operator. We use the methods of Trace Dynamics to construct a non-commutative special relativity. We define a line-element using the Trace over space-time coordinates which are assumed to be operators. The line-element is shown to be invariant under standard Lorentz transformations, and is used to construct a non-commutative relativistic dynamics. The eventual motivation for constructing such a non-commutative relativity is to relate the statistical thermodynamics of this classical theory to quantum mechanics. -- Highlights: → Classical time is external to quantum mechanics. → This implies need for a formulation of quantum theory without classical time. → A starting point could be a non-commutative special relativity. → Such a relativity is developed here using the theory of Trace Dynamics. → A line-element is defined using the Trace over non-commuting space-time operators.
Quantum theory of noncommutative fields

International Nuclear Information System (INIS)

Carmona, J.M.; Cortes, J.L.; Gamboa, J.; Mendez, F.

2003-01-01

Generalizing the noncommutative harmonic oscillator construction, we propose a new extension of quantum field theory based on the concept of 'noncommutative fields'. Our description permits to break the usual particle-antiparticle degeneracy at the dispersion relation level and introduces naturally an ultraviolet and an infrared cutoff. Phenomenological bounds for these new energy scales are given. (author)
Geometry, topology, and string theory

Energy Technology Data Exchange (ETDEWEB)

Varadarajan, Uday [Univ. of California, Berkeley, CA (United States)

2003-01-01

A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.
Geometry, topology, and string theory

International Nuclear Information System (INIS)

Varadarajan, Uday

2003-01-01

A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated
Unity from duality: gravity, gauge theory and strings

International Nuclear Information System (INIS)

Bachas, C.; Bilal, A.; Douglas, M.; Nekrasov, N.; David, F.

2002-01-01

The 76. session of the summer school in theoretical physics was devoted to recent developments in string theory, gauge theories and quantum gravity. Superstring theory is the leading candidate for a unified theory of all fundamental physical forces and elementary particles. The discovery of dualities and of important tools such as D-branes, has greatly reinforced this point of view. This document gathers the papers of 9 lectures: 1) supergravity, 2) supersymmetric gauge theories, 3) an introduction to duality symmetries, 4) large N field theories and gravity, 5) D-branes on the conifold and N = 1 gauge/gravity dualities, 6) de Sitter space, 7) string compactification with N = 1 supersymmetry, 8) open strings and non-commutative gauge theories, and 9) condensates near the Argyres-Douglas point in SU(2) gauge theory with broken N = 2 supersymmetry, and of 8 seminars: 1) quantum field theory with extra dimensions, 2) special holonomy spaces and M-theory, 3) four dimensional non-critical strings, 4) U-opportunities: why ten equal to ten?, 5) exact answers to approximate questions - non-commutative dipoles, open Wilson lines and UV-IR duality, 6) open-string models with broken supersymmetry, 7) on a field theory of open strings, tachyon condensation and closed strings, and 8) exceptional magic. (A.C.)
Abelian Toda field theories on the noncommutative plane

Science.gov (United States)

Cabrera-Carnero, Iraida

2005-10-01

Generalizations of GL(n) abelian Toda and GL with tilde above(n) abelian affine Toda field theories to the noncommutative plane are constructed. Our proposal relies on the noncommutative extension of a zero-curvature condition satisfied by algebra-valued gauge potentials dependent on the fields. This condition can be expressed as noncommutative Leznov-Saveliev equations which make possible to define the noncommutative generalizations as systems of second order differential equations, with an infinite chain of conserved currents. The actions corresponding to these field theories are also provided. The special cases of GL(2) Liouville and GL with tilde above(2) sinh/sine-Gordon are explicitly studied. It is also shown that from the noncommutative (anti-)self-dual Yang-Mills equations in four dimensions it is possible to obtain by dimensional reduction the equations of motion of the two-dimensional models constructed. This fact supports the validity of the noncommutative version of the Ward conjecture. The relation of our proposal to previous versions of some specific Toda field theories reported in the literature is presented as well.
On noncommutative open string theories

International Nuclear Information System (INIS)

Russo, J.G.; Sheikh-Jabbari, M.M.

2000-08-01

We investigate new compactifications of OM theory giving rise to a 3+1 dimensional open string theory with noncommutative x 0 -x 1 and x 2 -x 3 coordinates. The theory can be directly obtained by starting with a D3 brane with parallel (near critical) electric and magnetic field components, in the presence of a RR scalar field. The magnetic parameter permits to interpolate continuously between the x 0 -x 1 noncommutative open string theory and the x 2 -x 3 spatial noncommutative U(N) super Yang-Mills theory. We discuss SL(2, Z) transformations of this theory. Using the supergravity description of the large N limit, we also compute corrections to the quark-antiquark Coulomb potential arising in the NCOS theory. (author)
Two-dimensional black holes and non-commutative spaces

International Nuclear Information System (INIS)

Sadeghi, J.

2008-01-01

We study the effects of non-commutative spaces on two-dimensional black hole. The event horizon of two-dimensional black hole is obtained in non-commutative space up to second order of perturbative calculations. A lower limit for the non-commutativity parameter is also obtained. The observer in that limit in contrast to commutative case see two horizon
A noncommutative catenoid

Science.gov (United States)

Arnlind, Joakim; Holm, Christoffer

2018-01-01

A noncommutative algebra corresponding to the classical catenoid is introduced together with a differential calculus of derivations. We prove that there exists a unique metric and torsion-free connection that is compatible with the complex structure, and the curvature is explicitly calculated. A noncommutative analogue of the fact that the catenoid is a minimal surface is studied by constructing a Laplace operator from the connection and showing that the embedding coordinates are harmonic. Furthermore, an integral is defined and the total curvature is computed. Finally, classes of left and right modules are introduced together with constant curvature connections, and bimodule compatibility conditions are discussed in detail.
Holographic complexity and noncommutative gauge theory

Science.gov (United States)

Couch, Josiah; Eccles, Stefan; Fischler, Willy; Xiao, Ming-Lei

2018-03-01

We study the holographic complexity of noncommutative field theories. The four-dimensional N=4 noncommutative super Yang-Mills theory with Moyal algebra along two of the spatial directions has a well known holographic dual as a type IIB supergravity theory with a stack of D3 branes and non-trivial NS-NS B fields. We start from this example and find that the late time holographic complexity growth rate, based on the "complexity equals action" conjecture, experiences an enhancement when the non-commutativity is turned on. This enhancement saturates a new limit which is exactly 1/4 larger than the commutative value. We then attempt to give a quantum mechanics explanation of the enhancement. Finite time behavior of the complexity growth rate is also studied. Inspired by the non-trivial result, we move on to more general setup in string theory where we have a stack of D p branes and also turn on the B field. Multiple noncommutative directions are considered in higher p cases.

Photon defects in noncommutative standard model candidates

International Nuclear Information System (INIS)

Abel, S.A.; Khoze, V.V.

2006-06-01

Restrictions imposed by gauge invariance in noncommutative spaces together with the effects of ultraviolet/infrared mixing lead to strong constraints on possible candidates for a noncommutative extension of the Standard Model. We study a general class of noncommutative models consistent with these restrictions. Specifically we consider models based upon a gauge theory with the gauge group U(N 1 ) x U(N 2 ) x.. x U(N m ) coupled to matter fields transforming in the (anti)-fundamental, bi-fundamental and adjoint representations. We pay particular attention to overall trace-U(1) factors of the gauge group which are affected by the ultraviolet/infrared mixing. Typically, these trace-U(1) gauge fields do not decouple sufficiently fast in the infrared, and lead to sizable Lorentz symmetry violating effects in the low-energy effective theory. In a 4-dimensional theory on a continuous space-time making these effects unobservable would require making the effects of noncommutativity tiny, M NC >> M P . This severely limits the phenomenological prospects of such models. However, adding additional universal extra dimensions the trace-U(1) factors decouple with a power law and the constraint on the noncommutativity scale is weakened considerably. Finally, we briefly mention some interesting properties of the photon that could arise if the noncommutative theory is modified at a high energy scale. (Orig.)
Noncommutative de Sitter and FRW spaces

International Nuclear Information System (INIS)

Burić, Maja; Madore, John

2015-01-01

Several versions of fuzzy four-dimensional de Sitter space are constructed using the noncommutative frame formalism. Although all noncommutative spacetimes which are found have commutative de Sitter metric as a classical limit, the algebras and the differential calculi which define them have many differences, which we derive and discuss
Hopf algebras in noncommutative geometry

International Nuclear Information System (INIS)

Varilly, Joseph C.

2001-10-01

We give an introductory survey to the use of Hopf algebras in several problems of non- commutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We show its relation to the algebra of transverse differential operators introduced by Connes and Moscovici in order to compute a local index formula in cyclic cohomology, and to the several Hopf algebras defined by Connes and Kreimer to simplify the combinatorics of perturbative renormalization. We explain how characteristic classes for a Hopf module algebra can be obtained from the cyclic cohomology of the Hopf algebra which acts on it. Finally, we discuss the theory of non- commutative spherical manifolds and show how they arise as homogeneous spaces of certain compact quantum groups. (author)
Thermodynamic geometry of black holes in f(R) gravity

International Nuclear Information System (INIS)

Soroushfar, Saheb; Saffari, Reza; Kamvar, Negin

2016-01-01

In this paper, we consider three types (static, static charged, and rotating charged) of black holes in f(R) gravity. We study the thermodynamical behavior, stability conditions, and phase transition of these black holes. It is shown that the number and type of phase transition points are related to different parameters, which shows the dependency of the stability conditions to these parameters. Also, we extend our study to different thermodynamic geometry methods (Ruppeiner, Weinhold, and GTD). Next, we investigate the compatibility of curvature scalar of geothermodynamic methods with phase transition points of the above black holes. In addition, we point out the effect of different values of the spacetime parameters on the stability conditions of mentioned black holes. (orig.)
Geometric Description of the Thermodynamics of the Noncommutative Schwarzschild Black Hole

Directory of Open Access Journals (Sweden)

Alexis Larrañaga

2013-01-01

Full Text Available The thermodynamics of the noncommutative Schwarzschild black hole is reformulated within the context of the recently developed formalism of geometrothermodynamics (GTD. Using a thermodynamic metric which is invariant with respect to Legendre transformations, we determine the geometry of the space of equilibrium states and show that phase transitions, which correspond to divergencies of the heat capacity, are represented geometrically as singularities of the curvature scalar. This further indicates that the curvature of the thermodynamic metric is a measure of thermodynamic interaction.
Deformation quantization of noncommutative quantum mechanics and dissipation

Energy Technology Data Exchange (ETDEWEB)

Bastos, C [Departamento de Fisica, Instituto Superior Tecnico, Avenida Rovisco Pais 1, 1049-001 Lisbon (Portugal); Bertolami, O [Departamento de Fisica, Instituto Superior Tecnico, Avenida Rovisco Pais 1, 1049-001 Lisbon (Portugal); Dias, N C [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Avenida Campo Grande 376, 1749-024 Lisbon (Portugal); Prata, J N [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Avenida Campo Grande 376, 1749-024 Lisbon (Portugal)

2007-05-15

We review the main features of the Weyl-Wigner formulation of noncommutative quantum mechanics. In particular, we present a *-product and a Moyal bracket suitable for this theory as well as the concept of noncommutative Wigner function. The properties of these quasi-distributions are discussed as well as their relation to the sets of ordinary Wigner functions and positive Liouville probability densities. Based on these notions we propose criteria for assessing whether a commutative regime has emerged in the realm of noncommutative quantum mechanics. To induce this noncommutative-commutative transition, we couple a particle to an external bath of oscillators. The master equation for the Brownian particle is deduced.
Noncommutative quantum mechanics and Bohm's ontological interpretation

International Nuclear Information System (INIS)

Barbosa, G.D.; Pinto-Neto, N.

2004-01-01

We carry out an investigation into the possibility of developing a Bohmian interpretation based on the continuous motion of point particles for noncommutative quantum mechanics. The conditions for such an interpretation to be consistent are determined, and the implications of its adoption for noncommutativity are discussed. A Bohmian analysis of the noncommutative harmonic oscillator is carried out in detail. By studying the particle motion in the oscillator orbits, we show that small-scale physics can have influence at large scales, something similar to the IR-UV mixing
Noncommutative quantum scattering in a central field

International Nuclear Information System (INIS)

Bellucci, Stefano; Yeranyan, Armen

2005-01-01

In this Letter the problem of noncommutative elastic scattering in a central field is considered. General formulas for the differential cross-section for two cases are obtained. For the case of high energy of an incident wave it is shown that the differential cross-section coincides with that on the commutative space. For the case in which noncommutativity yields only a small correction to the central potential it is shown that the noncommutativity leads to the redistribution of particles along the azimuthal angle, although the whole cross-section coincides with the commutative case
Noncommutative gauge theories and Kontsevich's formality theorem

International Nuclear Information System (INIS)

Jurco, B.; Schupp, P.; Wess, J.

2001-01-01

The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map.) Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; as a byproduct we obtain a 'Mini Seiberg-Witten map' that explicitly relates ordinary abelian and nonabelian gauge fields. All constructions are also valid for non-constant B-field, and even more generally for any Poisson tensor
Cancellation of soft and collinear divergences in noncommutative QED

International Nuclear Information System (INIS)

Mirza, B.; Zarei, M.

2006-01-01

In this paper, we investigate the behavior of noncommutative IR divergences and will also discuss their cancellation in the physical cross sections. The commutative IR (soft) divergences existing in the nonplanar diagrams will be examined in order to prove an all-order cancellation of these divergences using the Weinberg's method. In noncommutative QED, collinear divergences due to triple photon splitting vertex, were encountered, which are shown to be canceled out by the noncommutative version of KLN theorem. This guarantees that there is no mixing between the Collinear, soft divergences and noncommutative IR divergences
Exact master equation for a noncommutative Brownian particle

International Nuclear Information System (INIS)

Costa Dias, Nuno; Nuno Prata, Joao

2009-01-01

We derive the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators on the plane with spatial noncommutativity. The results obtained are exact to all orders in the noncommutative parameter. As a by-product we derive some miscellaneous results such as the equilibrium Wigner distribution for the reservoir of noncommutative oscillators, the weak coupling limit of the master equation and a set of sufficient conditions for strict purity decrease of the Brownian particle. Finally, we consider a high-temperature Ohmic model and obtain an estimate for the time scale of the transition from noncommutative to ordinary quantum mechanics. This scale is considerably smaller than the decoherence scale
Noncommutative SO(n) and Sp(n) gauge theories

International Nuclear Information System (INIS)

Bonora, L.; INFN, Sezione di Trieste, Trieste; Schnabl, M.; INFN, Sezione di Trieste, Trieste; Sheikh-Jabbari, M.M.; Tomasiello, A.

2000-08-01

We study the generalization of noncommutative gauge theories to the case of orthogonal and symplectic groups. We find out that this is possible, since we are allowed to define orthogonal and symplectic subgroups of noncommutative unitary gauge transformations even though the gauge potentials and gauge transformations are not valued in the orthogonal and symplectic subalgebras of the Lie algebra of antihermitean matrices. Our construction relies on an antiautomorphism of the basic noncommutative algebra of functions which generalizes the charge conjugation operator of ordinary field theory. We show that the corresponding noncommutative picture from low energy string theory is obtained via orientifold projection in the presence of a non-trivial NSNS B-field. (author)
Quantum electrodynamics with arbitrary charge on a noncommutative space

International Nuclear Information System (INIS)

Zhou Wanping; Long Zhengwen; Cai Shaohong

2009-01-01

Using the Seiberg-Witten map, we obtain a quantum electrodynamics on a noncommutative space, which has arbitrary charge and keep the gauge invariance to at the leading order in theta. The one-loop divergence and Compton scattering are reinvestigated. The noncommutative effects are larger than those in ordinary noncommutative quantum electrodynamics. (authors)
Black-body radiation of noncommutative gauge fields

International Nuclear Information System (INIS)

Fatollahi, Amir H.; Hajirahimi, Maryam

2006-01-01

The black-body radiation is considered in a theory with noncommutative electRomegnetic fields; that is noncommutativity is introduced in field space, rather than in real space. A direct implication of the result on cosmic microwave background map is argued
Towards Noncommutative Linking Numbers via the Seiberg-Witten Map

Directory of Open Access Journals (Sweden)

H. García-Compeán

2015-01-01

Full Text Available Some geometric and topological implications of noncommutative Wilson loops are explored via the Seiberg-Witten map. In the abelian Chern-Simons theory on a three-dimensional manifold, it is shown that the effect of noncommutativity is the appearance of 6n new knots at the nth order of the Seiberg-Witten expansion. These knots are trivial homology cycles which are Poincaré dual to the higher-order Seiberg-Witten potentials. Moreover the linking number of a standard 1-cycle with the Poincaré dual of the gauge field is shown to be written as an expansion of the linking number of this 1-cycle with the Poincaré dual of the Seiberg-Witten gauge fields. In the process we explicitly compute the noncommutative “Jones-Witten” invariants up to first order in the noncommutative parameter. Finally in order to exhibit a physical example, we apply these ideas explicitly to the Aharonov-Bohm effect. It is explicitly displayed at first order in the noncommutative parameter; we also show the relation to the noncommutative Landau levels.
Quantum groups, non-commutative differential geometry and applications

International Nuclear Information System (INIS)

Schupp, P.; California Univ., Berkeley, CA

1993-01-01

The topic of this thesis is the development of a versatile and geometrically motivated differential calculus on non-commutative or quantum spaces, providing powerful but easy-to-use mathematical tools for applications in physics and related sciences. A generalization of unitary time evolution is proposed and studied for a simple 2-level system, leading to non-conservation of microscopic entropy, a phenomenon new to quantum mechanics. A Cartan calculus that combines functions, forms, Lie derivatives and inner derivations along general vector fields into one big algebra is constructed for quantum groups and then extended to quantum planes. The construction of a tangent bundle on a quantum group manifold and an BRST type approach to quantum group gauge theory are given as further examples of applications. The material is organized in two parts: Part I studies vector fields on quantum groups, emphasizing Hopf algebraic structures, but also introducing a ''quantum geometric'' construction. Using a generalized semi-direct product construction we combine the dual Hopf algebras A of functions and U of left-invariant vector fields into one fully bicovariant algebra of differential operators. The pure braid group is introduced as the commutant of Δ(U). It provides invariant maps A → U and thereby bicovariant vector fields, casimirs and metrics. This construction allows the translation of undeformed matrix expressions into their less obvious quantum algebraic counter parts. We study this in detail for quasitriangular Hopf algebras, giving the determinant and orthogonality relation for the ''reflection'' matrix. Part II considers the additional structures of differential forms and finitely generated quantum Lie algebras -- it is devoted to the construction of the Cartan calculus, based on an undeformed Cartan identity
Non-commutativity in polar coordinates

Energy Technology Data Exchange (ETDEWEB)

Edwards, James P. [Universidad Michoacana de San Nicolas de Hidalgo, Ciudad Universitaria, Instituto de Fisica y Matematicas, Morelia, Michoacan (Mexico)

2017-05-15

We reconsider the fundamental commutation relations for non-commutative R{sup 2} described in polar coordinates with non-commutativity parameter θ. Previous analysis found that the natural transition from Cartesian coordinates to the traditional polar system led to a representation of [r, φ] as an everywhere diverging series. In this article we compute the Borel resummation of this series, showing that it can subsequently be extended throughout parameter space and hence provide an interpretation of this commutator. Our analysis provides a complete solution for arbitrary r and θ that reproduces the earlier calculations at lowest order and benefits from being generally applicable to problems in a two-dimensional non-commutative space. We compare our results to previous literature in the (pseudo-)commuting limit, finding a surprising spatial dependence for the coordinate commutator when θ >> r{sup 2}. Finally, we raise some questions for future study in light of this progress. (orig.)
Time-space noncommutativity: quantised evolutions

International Nuclear Information System (INIS)

Balachandran, Aiyalam P.; Govindarajan, Thupil R.; Teotonio-Sobrinho, Paulo; Martins, Andrey Gomes

2004-01-01

In previous work, we developed quantum physics on the Moyal plane with time-space noncommutativity, basing ourselves on the work of Doplicher et al. Here we extend it to certain noncommutative versions of the cylinder, R 3 and Rx S 3 . In all these models, only discrete time translations are possible, a result known before in the first two cases. One striking consequence of quantised time translations is that even though a time independent hamiltonian is an observable, in scattering processes, it is conserved only modulo 2π/θ, where θ is the noncommutative parameter. (In contrast, on a one-dimensional periodic lattice of lattice spacing a and length L = Na, only momentum mod 2π/L is observable (and can be conserved).) Suggestions for further study of this effect are made. Scattering theory is formulated and an approach to quantum field theory is outlined. (author)
Noncommutative mathematics for quantum systems

CERN Document Server

Franz, Uwe

2016-01-01

Noncommutative mathematics is a significant new trend of mathematics. Initially motivated by the development of quantum physics, the idea of 'making theory noncommutative' has been extended to many areas of pure and applied mathematics. This book is divided into two parts. The first part provides an introduction to quantum probability, focusing on the notion of independence in quantum probability and on the theory of quantum stochastic processes with independent and stationary increments. The second part provides an introduction to quantum dynamical systems, discussing analogies with fundamental problems studied in classical dynamics. The desire to build an extension of the classical theory provides new, original ways to understand well-known 'commutative' results. On the other hand the richness of the quantum mathematical world presents completely novel phenomena, never encountered in the classical setting. This book will be useful to students and researchers in noncommutative probability, mathematical physi...
Towards the gravity/CYBE correspondence — the current status —

International Nuclear Information System (INIS)

Matsumoto, Takuya; Yoshida, Kentaroh

2016-01-01

We give a brief summary of Yang-Baxter deformations of the AdS 5 × S 5 superstring by focusing upon four examples, 1) gravity duals for noncommutative gauge theories, 2) γ-deformations of S 5 , 3) Schrödinger spacetimes and 4) abelian twists of the global AdS 5 . (paper)

Continual Lie algebras and noncommutative counterparts of exactly solvable models

Science.gov (United States)

Zuevsky, A.

2004-01-01

Noncommutative counterparts of exactly solvable models are introduced on the basis of a generalization of Saveliev-Vershik continual Lie algebras. Examples of noncommutative Liouville and sin/h-Gordon equations are given. The simplest soliton solution to the noncommutative sine-Gordon equation is found.
Paired quantum Hall states on noncommutative two-tori

Energy Technology Data Exchange (ETDEWEB)

Marotta, Vincenzo [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' and INFN, Sezione di Napoli, Compl. universitario M. Sant' Angelo, Via Cinthia, 80126 Napoli (Italy); Naddeo, Adele, E-mail: naddeo@sa.infn.i [CNISM, Unita di Ricerca di Salerno and Dipartimento di Fisica ' E. R. Caianiello' , Universita degli Studi di Salerno, Via Salvador Allende, 84081 Baronissi (Italy)

2010-08-01

By exploiting the notion of Morita equivalence for field theories on noncommutative tori and choosing rational values of the noncommutativity parameter theta (in appropriate units), a one-to-one correspondence between an Abelian noncommutative field theory (NCFT) and a non-Abelian theory of twisted fields on ordinary space can be established. Starting from this general result, we focus on the conformal field theory (CFT) describing a quantum Hall fluid (QHF) at paired states fillings nu=m/(pm+2) Cristofano et al. (2000) , recently obtained by means of m-reduction procedure, and show that it is the Morita equivalent of a NCFT. In this way we extend the construction proposed in Marotta and Naddeo (2008) for the Jain series nu=m/(2pm+1) . The case m=2 is explicitly discussed and the role of noncommutativity in the physics of quantum Hall bilayers is emphasized. Our results represent a step forward the construction of a new effective low energy description of certain condensed matter phenomena and help to clarify the relationship between noncommutativity and quantum Hall fluids.
Nucleon structure functions in noncommutative space-time

Energy Technology Data Exchange (ETDEWEB)

Rafiei, A.; Rezaei, Z.; Mirjalili, A. [Yazd University, Physics Department, Yazd (Iran, Islamic Republic of)

2017-05-15

In the context of noncommutative space-time we investigate the nucleon structure functions which play an important role in identifying the internal structure of nucleons. We use the corrected vertices and employ new vertices that appear in two approaches of noncommutativity and calculate the proton structure functions in terms of the noncommutative tensor θ{sub μν}. To check our results we plot the nucleon structure function (NSF), F{sub 2}(x), and compare it with experimental data and the results from the GRV, GJR and CT10 parametrization models. We show that with the new vertex that arises the noncommutativity correction will lead to a better consistency between theoretical results and experimental data for the NSF. This consistency will be better for small values of the Bjorken variable x. To indicate and confirm the validity of our calculations we also act conversely. We obtain a lower bound for the numerical values of Λ{sub NC} scale which correspond to recent reports. (orig.)
Discrete symmetries (C,P,T) in noncommutative field theories

International Nuclear Information System (INIS)

Sheikh-Jabbari, M.M.

2000-01-01

In this paper we study the invariance of the noncommutative gauge theories tinder C, P and T transformations. For the noncommutative space (when only the spatial part of θ is non-zero) we show that NCQED is Parity invariant. In addition, we show that under charge conjugation the theory on noncommutative R θ 4 is transformed to the theory on R -θ 4 , so NCQED is a CP violating theory. The theory remains invariant under time reversal if, together with proper changes in fields, we also change θ by -θ. Hence altogether NCQED is CPT invariant. Moreover we show that the CPT invariance holds for general noncommutative space-time. (author)
Noncommutative gauge theory for Poisson manifolds

Energy Technology Data Exchange (ETDEWEB)

Jurco, Branislav E-mail: jurco@mpim-bonn.mpg.de; Schupp, Peter E-mail: schupp@theorie.physik.uni-muenchen.de; Wess, Julius E-mail: wess@theorie.physik.uni-muenchen.de

2000-09-25

A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem.
Noncommutative gauge theory for Poisson manifolds

International Nuclear Information System (INIS)

Jurco, Branislav; Schupp, Peter; Wess, Julius

2000-01-01

A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem
Construction of non-Abelian gauge theories on noncommutative spaces

International Nuclear Information System (INIS)

Jurco, B.; Schupp, P.; Moeller, L.; Wess, J.; Max-Planck-Inst. fuer Physik, Muenchen; Humboldt-Univ., Berlin; Schraml, S.; Humboldt-Univ., Berlin

2001-01-01

We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories. (orig.)
Construction of non-Abelian gauge theories on noncommutative spaces

Energy Technology Data Exchange (ETDEWEB)

Jurco, B.; Schupp, P. [Sektion Physik, Muenchen Univ. (Germany); Moeller, L.; Wess, J. [Sektion Physik, Muenchen Univ. (Germany); Max-Planck-Inst. fuer Physik, Muenchen (Germany); Humboldt-Univ., Berlin (Germany). Inst. fuer Physik; Schraml, S. [Sektion Physik, Muenchen Univ. (Germany)

2001-06-01

We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories. (orig.)
Noncommutative geometry and the standard model vacuum

International Nuclear Information System (INIS)

Barrett, John W.; Dawe Martins, Rachel A.

2006-01-01

The space of Dirac operators for the Connes-Chamseddine spectral action for the standard model of particle physics coupled to gravity is studied. The model is extended by including right-handed neutrino states, and the S 0 -reality axiom is not assumed. The possibility of allowing more general fluctuations than the inner fluctuations of the vacuum is proposed. The maximal case of all possible fluctuations is studied by considering the equations of motion for the vacuum. While there are interesting nontrivial vacua with Majorana-type mass terms for the leptons, the conclusion is that the equations are too restrictive to allow solutions with the standard model mass matrix
Non-commutative and commutative vacua effects in a scalar torsion scenario

Energy Technology Data Exchange (ETDEWEB)

Sheikhahmadi, Haidar, E-mail: h.sh.ahmadi@gmail.com [Department of Physics, Faculty of Science, University of Kurdistan, Sanandaj (Iran, Islamic Republic of); Aghamohammadi, Ali, E-mail: a.aghamohamadi@iausdj.ac.ir [Sanandaj Branch, Islamic Azad University, Sanandaj (Iran, Islamic Republic of); Saaidi, Khaled, E-mail: ksaaidi@uok.ac.ir [Department of Physics, Faculty of Science, University of Kurdistan, Sanandaj (Iran, Islamic Republic of)

2015-10-07

In this work, the effects of non-commutative and commutative vacua on the phase space generated by a scalar field in a scalar torsion scenario are investigated. For both classical and quantum regimes, the commutative and non-commutative cases are compared. To take account the effects of non-commutativity, two well known non-commutative parameters, θ and β, are introduced. It should be emphasized, the effects of β which is related to momentum sector has more key role in comparison to θ which is related to space sector. Also the different boundary conditions and mathematical interpretations of non-commutativity are explored.
Non-commutative and commutative vacua effects in a scalar torsion scenario

International Nuclear Information System (INIS)

Sheikhahmadi, Haidar; Aghamohammadi, Ali; Saaidi, Khaled

2015-01-01

In this work, the effects of non-commutative and commutative vacua on the phase space generated by a scalar field in a scalar torsion scenario are investigated. For both classical and quantum regimes, the commutative and non-commutative cases are compared. To take account the effects of non-commutativity, two well known non-commutative parameters, θ and β, are introduced. It should be emphasized, the effects of β which is related to momentum sector has more key role in comparison to θ which is related to space sector. Also the different boundary conditions and mathematical interpretations of non-commutativity are explored.
FINAL REPORT: GEOMETRY AND ELEMENTARY PARTICLE PHYSICS

Energy Technology Data Exchange (ETDEWEB)

Singer, Isadore M.

2008-03-04

The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists’ quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energy for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.
Final Report: Geometry And Elementary Particle Physics

International Nuclear Information System (INIS)

Singer, Isadore M.

2008-01-01

The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energy for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.
Conformal quantum mechanics and holography in noncommutative space-time

Science.gov (United States)

Gupta, Kumar S.; Harikumar, E.; Zuhair, N. S.

2017-09-01

We analyze the effects of noncommutativity in conformal quantum mechanics (CQM) using the κ-deformed space-time as a prototype. Up to the first order in the deformation parameter, the symmetry structure of the CQM algebra is preserved but the coupling in a canonical model of the CQM gets deformed. We show that the boundary conditions that ensure a unitary time evolution in the noncommutative CQM can break the scale invariance, leading to a quantum mechanical scaling anomaly. We calculate the scaling dimensions of the two and three point functions in the noncommutative CQM which are shown to be deformed. The AdS2 / CFT1 duality for the CQM suggests that the corresponding correlation functions in the holographic duals are modified. In addition, the Breitenlohner-Freedman bound also picks up a noncommutative correction. The strongly attractive regime of a canonical model of the CQM exhibit quantum instability. We show that the noncommutativity softens this singular behaviour and its implications for the corresponding holographic duals are discussed.
An integrable noncommutative version of the sine-Gordon system

International Nuclear Information System (INIS)

Grisaru, Marcus T.; Penati, Silvia

2003-01-01

Using the bicomplex approach we discuss an integrable noncommutative system in two-dimensional Euclidean space. It is described by an equation of motion which reduces to the ordinary sine-Gordon equation when the noncommutation parameter is removed, plus a constraint equation which is nontrivial only in the noncommutative case. The implications of this constraint, which is required by integrability but seems to reduce the space of classical solutions, remain to be understood. We show that the system has an infinite number of conserved currents and we give the general recursive relation for constructing them. For the particular cases of lower spin nontrivial currents we work out the explicit expressions and perform a direct check of their conservation. These currents reduce to the usual sine-Gordon currents in the commutative limit. We find classical 'localized' solutions to first order in the noncommutativity parameter and describe the Backlund transformations for our system. Finally, we comment on the relation of our noncommutative system to the commutative sine-Gordon system
Quantum information aspects of noncommutative quantum mechanics

Science.gov (United States)

Bertolami, Orfeu; Bernardini, Alex E.; Leal, Pedro

2018-01-01

Some fundamental aspects related with the construction of Robertson-Schrödinger-like uncertainty-principle inequalities are reported in order to provide an overall description of quantumness, separability and nonlocality of quantum systems in the noncommutative phase-space. Some consequences of the deformed noncommutative algebra are also considered in physical systems of interest.
W-geometry

International Nuclear Information System (INIS)

Hull, C.M.

1993-01-01

The geometric structure of theories with gauge fields of spins two and higher should involve a higher spin generalisation of Riemannian geometry. Such geometries are discussed and the case of W ∝ -gravity is analysed in detail. While the gauge group for gravity in d dimensions is the diffeomorphism group of the space-time, the gauge group for a certain W-gravity theory (which is W ∝ -gravity in the case d=2) is the group of symplectic diffeomorphisms of the cotangent bundle of the space-time. Gauge transformations for W-gravity gauge fields are given by requiring the invariance of a generalised line element. Densities exist and can be constructed from the line element (generalising √detg μν ) only if d=1 or d=2, so that only for d=1,2 can actions be constructed. These two cases and the corresponding W-gravity actions are considered in detail. In d=2, the gauge group is effectively only a subgroup of the symplectic diffeomorphisms group. Some of the constraints that arise for d=2 are similar to equations arising in the study of self-dual four-dimensional geometries and can be analysed using twistor methods, allowing contact to be made with other formulations of W-gravity. While the twistor transform for self-dual spaces with one Killing vector reduces to a Legendre transform, that for two Killing vectors gives a generalisation of the Legendre transform. (orig.)
T-duality with H-flux. Non-commutativity, T-folds and G x G structure

International Nuclear Information System (INIS)

Grange, P.

2006-09-01

Various approaches to T-duality with NSNS three-form flux are reconciled. Non-commutative torus fibrations are shown to be the open-string version of T-folds. The non-geometric T-dual of a three-torus with uniform flux is embedded into a generalized complex six-torus, and the non-geometry is probed by D0-branes regarded as generalized complex submanifolds. The non-commutativity scale, which is present in these compactifications, is given by a holomorphic Poisson bivector that also encodes the variation of the dimension of the world-volume of D-branes under monodromy. This bivector is shown to exist in SU(3) x SU(3) structure compactifications, which have been proposed as mirrors to NSNS-flux backgrounds. The two SU(3)-invariant spinors are generically not parallel, thereby giving rise to a non-trivial Poisson bivector. Furthermore we show that for non-geometric T-duals, the Poisson bivector may not be decomposable into the tensor product of vectors. (orig.)
Noncommutative GUTs, Standard Model and C,P,T

International Nuclear Information System (INIS)

Aschieri, P.; Jurco, B.; Schupp, P.; Wess, J.

2003-01-01

Noncommutative Yang-Mills theories are sensitive to the choice of the representation that enters in the gauge kinetic term. We constrain this ambiguity by considering grand unified theories. We find that at first order in the noncommutativity parameter θ, SU(5) is not truly a unified theory, while SO(10) has a unique noncommutative generalization. In view of these results we discuss the noncommutative SM theory that is compatible with SO(10) GUT and find that there are no modifications to the SM gauge kinetic term at lowest order in θ. We study in detail the reality, Hermiticity and C,P,T properties of the Seiberg-Witten map and of the resulting effective actions expanded in ordinary fields. We find that in models of GUTs (or compatible with GUTs) right-handed fermions and left-handed ones appear with opposite Seiberg-Witten map
Noncommutative GUTs, Standard Model and C,P,T

Energy Technology Data Exchange (ETDEWEB)

Aschieri, P. E-mail: aschieri@theorie.physik.uni-muenchen.de; Jurco, B. E-mail: jurco@theorie.physik.uni-muenchen.de; Schupp, P. E-mail: p.schupp@iu-bremen.de; Wess, J. E-mail: wess@theorie.physik.uni-muenchen.de

2003-02-17

Noncommutative Yang-Mills theories are sensitive to the choice of the representation that enters in the gauge kinetic term. We constrain this ambiguity by considering grand unified theories. We find that at first order in the noncommutativity parameter {theta}, SU(5) is not truly a unified theory, while SO(10) has a unique noncommutative generalization. In view of these results we discuss the noncommutative SM theory that is compatible with SO(10) GUT and find that there are no modifications to the SM gauge kinetic term at lowest order in {theta}. We study in detail the reality, Hermiticity and C,P,T properties of the Seiberg-Witten map and of the resulting effective actions expanded in ordinary fields. We find that in models of GUTs (or compatible with GUTs) right-handed fermions and left-handed ones appear with opposite Seiberg-Witten map.

Deformed two-photon squeezed states in noncommutative space

International Nuclear Information System (INIS)

Zhang Jianzu

2004-01-01

Recent studies on nonperturbation aspects of noncommutative quantum mechanics explored a new type of boson commutation relations at the deformed level, described by deformed annihilation-creation operators in noncommutative space. This correlated boson commutator correlates different degrees of freedom, and shows an essential influence on dynamics. This Letter devotes to the development of formalism of deformed two-photon squeezed states in noncommutative space. General representations of deformed annihilation-creation operators and the consistency condition for the electromagnetic wave with a single mode of frequency in noncommunicative space are obtained. Two-photon squeezed states are studied. One finds that variances of the dimensionless Hermitian quadratures of the annihilation operator in one degree of freedom include variances in the other degree of freedom. Such correlations show the new feature of spatial noncommutativity and allow a deeper understanding of the correlated boson commutator
Properties of the center of gravity as an algorithm for position measurements: Two-dimensional geometry

CERN Document Server

Landi, Gregorio

2003-01-01

The center of gravity as an algorithm for position measurements is analyzed for a two-dimensional geometry. Several mathematical consequences of discretization for various types of detector arrays are extracted. Arrays with rectangular, hexagonal, and triangular detectors are analytically studied, and tools are given to simulate their discretization properties. Special signal distributions free of discretized error are isolated. It is proved that some crosstalk spreads are able to eliminate the center of gravity discretization error for any signal distribution. Simulations, adapted to the CMS em-calorimeter and to a triangular detector array, are provided for energy and position reconstruction algorithms with a finite number of detectors.
Non-commutative and commutative vacua effects in a scalar torsion scenario

Directory of Open Access Journals (Sweden)

Haidar Sheikhahmadi

2015-10-01

Full Text Available In this work, the effects of non-commutative and commutative vacua on the phase space generated by a scalar field in a scalar torsion scenario are investigated. For both classical and quantum regimes, the commutative and non-commutative cases are compared. To take account the effects of non-commutativity, two well known non-commutative parameters, θ and β, are introduced. It should be emphasized, the effects of β which is related to momentum sector has more key role in comparison to θ which is related to space sector. Also the different boundary conditions and mathematical interpretations of non-commutativity are explored.
Black Hole Complementary Principle and Noncommutative Membrane

International Nuclear Information System (INIS)

Wei Ren

2006-01-01

In the spirit of black hole complementary principle, we have found the noncommutative membrane of Scharzchild black holes. In this paper we extend our results to Kerr black hole and see the same story. Also we make a conjecture that spacetimes are noncommutative on the stretched membrane of the more general Kerr-Newman black hole.
Noncommutative black-body radiation: Implications on cosmic microwave background

International Nuclear Information System (INIS)

Fatollahi, A.H.; Hajirahimi, M.

2006-01-01

Including loop corrections, black-body radiation in noncommutative space is anisotropic. A direct implication of possible space non-commutativity on the cosmic microwave background map is argued. (authors)
The Event Horizon of The Schwarzschild Black Hole in Noncommutative Spaces

OpenAIRE

Nasseri, Forough

2005-01-01

The event horizon of Schwarzschild black hole is obtained in noncommutative spaces up to the second order of perturbative calculations. Because this type of black hole is non-rotating, to the first order there is no any effect on the event horizon due to the noncommutativity of space. A lower limit for the noncommutativity parameter is also obtained. As a result, the event horizon in noncommutative spaces is less than the event horizon in commutative spaces.
Some aspects of noncommutative integrable systems a la Moyal

International Nuclear Information System (INIS)

Dafounansou, O.; El Boukili, A.; Sedra, M.B.

2005-12-01

Besides its various applications in string and D-brane physics, the non commutativity of space (-time) coordinates, based on the *-product, behaves as a more general framework providing more mathematical and physical information about the associated system. Similar to the Gelfand-Dickey framework of pseudo differential operators, the non commutativity a la Moyal applied to physical problems makes the study more systematic. Using these facts, as well as the backgrounds of Moyal momentum algebra introduced in previous works, we look for the important task of studying integrability in the noncommutativity framework. The main focus is on the noncommutative version of the Lax representation of two principal examples: the noncommutative sl 2 KdV equation and the noncommutative version of Burgers systems. Important properties are presented. (author)
Moving mirrors and black hole evaporation in noncommutative space-times

International Nuclear Information System (INIS)

Casadio, R.; Cox, P.H.; Harms, B.; Micu, O.

2006-01-01

We study the evaporation of black holes in noncommutative space-times. We do this by calculating the correction to the detector's response function for a moving mirror in terms of the noncommutativity parameter Θ and then extracting the number density as modified by this parameter. We find that allowing space and time to be noncommutative increases the decay rate of a black hole
Non-commutative tomography and signal processing

International Nuclear Information System (INIS)

Mendes, R Vilela

2015-01-01

Non-commutative tomography is a technique originally developed and extensively used by Professors M A Man’ko and V I Man’ko in quantum mechanics. Because signal processing deals with operators that, in general, do not commute with time, the same technique has a natural extension to this domain. Here, a review is presented of the theory and some applications of non-commutative tomography for time series as well as some new results on signal processing on graphs. (paper)
On noncommutativity with bifermionic parameter

International Nuclear Information System (INIS)

Acatrinei, Ciprian Sorin

2008-01-01

Recently Gitman and Vassilevich proposed an interesting model of noncommutative (NC) scalar field theory, with a noncommutativity parameter assumed to be the product of two Grassmann variables. They showed in particular that the model possesses a local energy-momentum tensor. Since such a property is quite unusual for a NC model, we provide here an alternative picture, based on an operatorial formulation of NC field theory. It leads to complete locality of the degrees of freedom of the theory, a property in agreement with the termination of the star-product at the second term in its series. (author)
Pair production by a constant external field in noncommutative QED

International Nuclear Information System (INIS)

Chair, N.; Sheikh-Jabbari, M.M.

2000-09-01

In this paper we study QED on the noncommutative space in the constant electro-magnetic field background. Using the explicit solutions of the noncommutative version of Dirac equation in such background, we show that there are well-defined in and out-going asymptotic states and also there is a causal Green's function. We calculate the pair production rate in this case. We show that at tree level noncommutativity will not change the pair production and the threshold electric field. We also calculate the pair production rate considering the first loop corrections. In this case we show that the threshold electric field is decreased by the noncommutativity effects. (author)
Quantum Field Theory with a Minimal Length Induced from Noncommutative Space

International Nuclear Information System (INIS)

Lin Bing-Sheng; Chen Wei; Heng Tai-Hua

2014-01-01

From the inspection of noncommutative quantum mechanics, we obtain an approximate equivalent relation for the energy dependence of the Planck constant in the noncommutative space, which means a minimal length of the space. We find that this relation is reasonable and it can inherit the main properties of the noncommutative space. Based on this relation, we derive the modified Klein—Gordon equation and Dirac equation. We investigate the scalar field and ϕ 4 model and then quantum electrodynamics in our theory, and derive the corresponding Feynman rules. These results may be considered as reasonable approximations to those of noncommutative quantum field theory. Our theory also shows a connection between the space with a minimal length and the noncommutative space. (physics of elementary particles and fields)
Dispersion relations in quantum electrodynamics on the noncommutative Minkowski space

Energy Technology Data Exchange (ETDEWEB)

Zahn, J.W.

2006-12-15

We study field theories on the noncommutative Minkowski space with noncommuting time. The focus lies on dispersion relations in quantized interacting models in the Yang-Feldman formalism. In particular, we compute the two-point correlation function of the field strength in noncommutative quantum electrodynamics to second order. At this, we take into account the covariant coordinates that allow the construction of local gauge invariant quantities (observables). It turns out that this does not remove the well-known severe infrared problem, as one might have hoped. Instead, things become worse, since nonlocal divergences appear. We also show that these cancel in a supersymmetric version of the theory if the covariant coordinates are adjusted accordingly. Furthermore, we study the {phi}{sup 3} and the Wess-Zumino model and show that the distortion of the dispersion relations is moderate for parameters typical for the Higgs field. We also discuss the formulation of gauge theories on noncommutative spaces and study classical electrodynamics on the noncommutative Minkowski space using covariant coordinates. In particular, we compute the change of the speed of light due to nonlinear effects in the presence of a background field. Finally, we examine the so-called twist approach to quantum field theory on the noncommutative Minkowski space and point out some conceptual problems of this approach. (orig.)
Dispersion relations in quantum electrodynamics on the noncommutative Minkowski space

International Nuclear Information System (INIS)

Zahn, J.W.

2006-12-01

We study field theories on the noncommutative Minkowski space with noncommuting time. The focus lies on dispersion relations in quantized interacting models in the Yang-Feldman formalism. In particular, we compute the two-point correlation function of the field strength in noncommutative quantum electrodynamics to second order. At this, we take into account the covariant coordinates that allow the construction of local gauge invariant quantities (observables). It turns out that this does not remove the well-known severe infrared problem, as one might have hoped. Instead, things become worse, since nonlocal divergences appear. We also show that these cancel in a supersymmetric version of the theory if the covariant coordinates are adjusted accordingly. Furthermore, we study the Φ 3 and the Wess-Zumino model and show that the distortion of the dispersion relations is moderate for parameters typical for the Higgs field. We also discuss the formulation of gauge theories on noncommutative spaces and study classical electrodynamics on the noncommutative Minkowski space using covariant coordinates. In particular, we compute the change of the speed of light due to nonlinear effects in the presence of a background field. Finally, we examine the so-called twist approach to quantum field theory on the noncommutative Minkowski space and point out some conceptual problems of this approach. (orig.)
Unusual high-energy phenomenology of Lorentz-invariant noncommutative field theories

International Nuclear Information System (INIS)

Carone, Christopher D.; Kwee, Herry J.

2006-01-01

It has been suggested that one may construct a Lorentz-invariant noncommutative field theory by extending the coordinate algebra to additional, fictitious coordinates that transform nontrivially under the Lorentz group. Integration over these coordinates in the action produces a four-dimensional effective theory with Lorentz invariance intact. Previous applications of this approach, in particular, to a specific construction of noncommutative QED, have been studied only in a low-momentum approximation. Here we discuss Lorentz-invariant field theories in which the relevant physics can be studied without requiring an expansion in the inverse scale of noncommutativity. Qualitatively, we find that tree-level scattering cross sections are dramatically suppressed as the center-of-mass energy exceeds the scale of noncommutativity, that cross sections that are isotropic in the commutative limit can develop a pronounced angular dependence, and that nonrelativistic potentials (for example, the Coloumb potential) become nonsingular at the origin. We consider a number of processes in noncommutative QED that may be studied at a future linear collider. We also give an example of scattering via a four-fermion operator in which the noncommutative modifications of the interaction can unitarize the tree-level amplitude, without requiring any other new physics in the ultraviolet
Noncommutative Gauge Theory with Covariant Star Product

International Nuclear Information System (INIS)

Zet, G.

2010-01-01

We present a noncommutative gauge theory with covariant star product on a space-time with torsion. In order to obtain the covariant star product one imposes some restrictions on the connection of the space-time. Then, a noncommutative gauge theory is developed applying this product to the case of differential forms. Some comments on the advantages of using a space-time with torsion to describe the gravitational field are also given.
Realization of Cohen-Glashow very special relativity on noncommutative space-time.

Science.gov (United States)

Sheikh-Jabbari, M M; Tureanu, A

2008-12-31

We show that the Cohen-Glashow very special relativity (VSR) theory [A. G. Cohen and S. L. Glashow, Phys. Rev. Lett. 97, 021601 (2006)] can be realized as the part of the Poincaré symmetry preserved on a noncommutative Moyal plane with lightlike noncommutativity. Moreover, we show that the three subgroups relevant to VSR can also be realized in the noncommutative space-time setting. For all of these three cases, the noncommutativity parameter theta(mu upsilon) should be lightlike (theta(mu upsilon) theta mu upsilon = 0). We discuss some physical implications of this realization of the Cohen-Glashow VSR.
A deformation quantization theory for noncommutative quantum mechanics

International Nuclear Information System (INIS)

Costa Dias, Nuno; Prata, Joao Nuno; Gosson, Maurice de; Luef, Franz

2010-01-01

We show that the deformation quantization of noncommutative quantum mechanics previously considered by Dias and Prata ['Weyl-Wigner formulation of noncommutative quantum mechanics', J. Math. Phys. 49, 072101 (2008)] and Bastos, Dias, and Prata ['Wigner measures in non-commutative quantum mechanics', e-print arXiv:math-ph/0907.4438v1; Commun. Math. Phys. (to appear)] can be expressed as a Weyl calculus on a double phase space. We study the properties of the star-product thus defined and prove a spectral theorem for the star-genvalue equation using an extension of the methods recently initiated by de Gosson and Luef ['A new approach to the *-genvalue equation', Lett. Math. Phys. 85, 173-183 (2008)].
Interacting open Wilson lines from noncommutative field theories

International Nuclear Information System (INIS)

Kiem, Youngjai; Lee, Sangmin; Rey, Soo-Jong; Sato, Haru-Tada

2002-01-01

In noncommutative field theories, it is known that the one-loop effective action describes the propagation of noninteracting open Wilson lines, obeying the flying dipole's relation. We show that the two-loop effective action describes the cubic interaction among 'closed string' states created by open Wilson line operators. Taking d-dimensional λ[Φ 3 ] * theory as the simplest setup, we compute the nonplanar contribution at a low-energy and large noncommutativity limit. We find that the contribution is expressible in a remarkably simple cubic interaction involving scalar open Wilson lines only and nothing else. We show that the interaction is purely geometrical and noncommutative in nature, depending only on the size of each open Wilson line
Recursive relations for processes with n photons of noncommutative QED

International Nuclear Information System (INIS)

Jafari, Abolfazl

2007-01-01

Recursion relations are derived in the sense of Berends-Giele for the multi-photon processes of noncommutative QED. The relations concern purely photonic processes as well as the processes with two fermions involved, both for arbitrary number of photons at tree level. It is shown that despite of the dependence of noncommutative vertices on momentum, in contrast to momentum-independent color factors of QCD, the recursion relation method can be employed for multi-photon processes of noncommutative QED

Dispersion relations for the self-energy in noncommutative field theories

International Nuclear Information System (INIS)

Brandt, F.T.; Das, Ashok; Frenkel, J.

2002-01-01

We study the IR-UV connection in noncommutative φ 3 theory as well as in noncommutative QED from the point of view of the dispersion relation for self-energy. We show that, although the imaginary part of the self-energy is well behaved as the parameter of noncommutativity vanishes, the real part becomes divergent as a consequence of the high energy behavior of the dispersion integral. Some other interesting features that arise from this analysis are also briefly discussed
Noncommutative gauge theory without Lorentz violation

International Nuclear Information System (INIS)

Carlson, Carl E.; Carone, Christopher D.; Zobin, Nahum

2002-01-01

The most popular noncommutative field theories are characterized by a matrix parameter θ μν that violates Lorentz invariance. We consider the simplest algebra in which the θ parameter is promoted to an operator and Lorentz invariance is preserved. This algebra arises through the contraction of a larger one for which explicit representations are already known. We formulate a star product and construct the gauge-invariant Lagrangian for Lorentz-conserving noncommutative QED. Three-photon vertices are absent in the theory, while a four-photon coupling exists and leads to a distinctive phenomenology
Differential Galois obstructions for non-commutative integrability

Energy Technology Data Exchange (ETDEWEB)

Maciejewski, Andrzej J. [Institute of Astronomy, University of Zielona Gora, Podgorna 50, PL-65-246 Zielona Gora (Poland)], E-mail: maciejka@astro.ia.uz.zgora.pl; Przybylska, Maria [Torun Centre for Astronomy, N. Copernicus University, Gagarina 11, PL-87-100 Torun (Poland)], E-mail: mprzyb@astri.uni.torun.pl

2008-08-11

We show that if a holomorphic Hamiltonian system is holomorphically integrable in the non-commutative sense in a neighbourhood of a non-equilibrium phase curve which is located at a regular level of the first integrals, then the identity component of the differential Galois group of the variational equations along the phase curve is Abelian. Thus necessary conditions for the commutative and non-commutative integrability given by the differential Galois approach are the same.
UV/IR mixing and the Goldstone theorem in noncommutative field theory

International Nuclear Information System (INIS)

Ruiz Ruiz, F.

2002-01-01

Noncommutative IR singularities and UV/IR mixing in relation with the Goldstone theorem for complex scalar field theory are investigated. The classical model has two coupling constants, λ 1 and λ 2 , associated to the two noncommutative extensions phi*starphistarphi* starphi and phistarphi*starphistarphi of the interaction term vertical bar phi vertical bar 4 on commutative spacetime. It is shown that the symmetric phase is one-loop renormalizable for all λ 1 and λ 2 compatible with perturbation theory, whereas the broken phase is proved to exist at one loop only if λ 2 =0, a condition required by the Ward identities for global U(1) invariance. Explicit expressions for the noncommutative IR singularities in the 1PI Green functions of both phases are given. They show that UV/IR duality does not hold for any of the phases and that the broken phase is free of quadratic noncommutative IR singularities. More remarkably, the pion selfenergy does not have noncommutative IR singularities at all, which proves essential to formulate the Goldstone theorem at one loop for all values of the spacetime noncommutativity parameter θ
Non-Commutative Mechanics in Mathematical & in Condensed Matter Physics

Directory of Open Access Journals (Sweden)

Peter A. Horváthy

2006-12-01

Full Text Available Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table 1. Souriau's construction applied to the two-parameter central extension of the planar Galilei group leads to the ''exotic'' particle, which has non-commuting position coordinates. A Berry-phase argument applied to the Bloch electron yields in turn a semiclassical model that has been used to explain the anomalous/spin/optical Hall effects. The non-commutative parameter is momentum-dependent in this case, and can take the form of a monopole in momentum space.
Soldering formalism in noncommutative field theory: a brief note

International Nuclear Information System (INIS)

Ghosh, Subir

2004-01-01

In this Letter, I develop the soldering formalism in a new domain--the noncommutative planar field theories. The soldering mechanism fuses two distinct theories showing opposite or complimentary properties of some symmetry, taking into account the interference effects. The above mentioned symmetry is hidden in the composite (or soldered) theory. In the present work it is shown that a pair of noncommutative Maxwell-Chern-Simons theories, having opposite signs in their respective topological terms, can be consistently soldered to yield the Proca model (Maxwell theory with a mass term) with corrections that are at least quadratic in the noncommutativity parameter. We further argue that this model can be thought of as the noncommutative generalization of the Proca theory of ordinary spacetime. It is well known that abelian noncommutative gauge theory bears a close structural similarity with non-abelian gauge theory. This fact is manifested in a non-trivial way if the present Letter is compared with existing literature, where soldering of non-abelian models are discussed. Thus the present work further establishes the robustness of the soldering programme. The subtle role played by gauge invariance (or the lack of it), in the above soldering process, is revealed in an interesting way
Differential geometry on Hopf algebras and quantum groups

International Nuclear Information System (INIS)

Watts, P.

1994-01-01

The differential geometry on a Hopf algebra is constructed, by using the basic axioms of Hopf algebras and noncommutative differential geometry. The space of generalized derivations on a Hopf algebra of functions is presented via the smash product, and used to define and discuss quantum Lie algebras and their properties. The Cartan calculus of the exterior derivative, Lie derivative, and inner derivation is found for both the universal and general differential calculi of an arbitrary Hopf algebra, and, by restricting to the quasitriangular case and using the numerical R-matrix formalism, the aforementioned structures for quantum groups are determined
On the classical dynamics of charges in non-commutative QED

International Nuclear Information System (INIS)

Fatollahi, A.H.; Mohammadzadeh, H.

2004-01-01

Following Wong's approach to formulating the classical dynamics of charged particles in non-Abelian gauge theories, we derive the classical equations of motion of a charged particle in U(1) gauge theory on non-commutative space, the so-called non-commutative QED. In the present use of the procedure, it is observed that the definition of the mechanical momenta should be modified. The derived equations of motion manifest the previous statement about the dipole behavior of the charges in non-commutative space. (orig.)
Dirac equation in noncommutative space for hydrogen atom

International Nuclear Information System (INIS)

Adorno, T.C.; Baldiotti, M.C.; Chaichian, M.; Gitman, D.M.; Tureanu, A.

2009-01-01

We consider the energy levels of a hydrogen-like atom in the framework of θ-modified, due to space noncommutativity, Dirac equation with Coulomb field. It is shown that on the noncommutative (NC) space the degeneracy of the levels 2S 1/2 , 2P 1/2 and 2P 3/2 is lifted completely, such that new transition channels are allowed.
Covariant Noncommutative Field Theory

Energy Technology Data Exchange (ETDEWEB)

Estrada-Jimenez, S [Licenciaturas en Fisica y en Matematicas, Facultad de Ingenieria, Universidad Autonoma de Chiapas Calle 4a Ote. Nte. 1428, Tuxtla Gutierrez, Chiapas (Mexico); Garcia-Compean, H [Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del IPN P.O. Box 14-740, 07000 Mexico D.F., Mexico and Centro de Investigacion y de Estudios Avanzados del IPN, Unidad Monterrey Via del Conocimiento 201, Parque de Investigacion e Innovacion Tecnologica (PIIT) Autopista nueva al Aeropuerto km 9.5, Lote 1, Manzana 29, cp. 66600 Apodaca Nuevo Leon (Mexico); Obregon, O [Instituto de Fisica de la Universidad de Guanajuato P.O. Box E-143, 37150 Leon Gto. (Mexico); Ramirez, C [Facultad de Ciencias Fisico Matematicas, Universidad Autonoma de Puebla, P.O. Box 1364, 72000 Puebla (Mexico)

2008-07-02

The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced.
Covariant Noncommutative Field Theory

International Nuclear Information System (INIS)

Estrada-Jimenez, S.; Garcia-Compean, H.; Obregon, O.; Ramirez, C.

2008-01-01

The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced
Geometry on the space of geometries

International Nuclear Information System (INIS)

Christodoulakis, T.; Zanelli, J.

1988-06-01

We discuss the geometric structure of the configuration space of pure gravity. This is an infinite dimensional manifold, M, where each point represents one spatial geometry g ij (x). The metric on M is dictated by geometrodynamics, and from it, the Christoffel symbols and Riemann tensor can be found. A ''free geometry'' tracing a geodesic on the manifold describes the time evolution of space in the strong gravity limit. In a regularization previously introduced by the authors, it is found that M does not have the same dimensionality, D, everywhere, and that D is not a scalar, although it is covariantly constant. In this regularization, it is seen that the path integral measure can be absorbed in a renormalization of the cosmological constant. (author). 19 refs
Noncommutative Gröbner bases and filtered-graded transfer

CERN Document Server

Li, Huishi

2002-01-01

This self-contained monograph is the first to feature the intersection of the structure theory of noncommutative associative algebras and the algorithmic aspect of Groebner basis theory. A double filtered-graded transfer of data in using noncommutative Groebner bases leads to effective exploitation of the solutions to several structural-computational problems, e.g., an algorithmic recognition of quadric solvable polynomial algebras, computation of GK-dimension and multiplicity for modules, and elimination of variables in noncommutative setting. All topics included deal with algebras of (q-)differential operators as well as some other operator algebras, enveloping algebras of Lie algebras, typical quantum algebras, and many of their deformations.
Causality and matter propagation in 3D spin foam quantum gravity

International Nuclear Information System (INIS)

Oriti, Daniele; Tlas, Tamer

2006-01-01

In this paper we tackle the issue of causality in quantum gravity, in the context of 3d spin foam models. We identify the correct procedure for implementing the causality/orientation dependence restriction that reduces the path integral for BF theory to that of quantum gravity in first order form. We construct explicitly the resulting causal spin foam model. We then add matter degrees of freedom to it and construct a causal spin foam model for 3d quantum gravity coupled to matter fields. Finally, we show that the corresponding spin foam amplitudes admit a natural approximation as the Feynman amplitudes of a noncommutative quantum field theory, with the appropriate Feynman propagators weighting the lines of propagation, and that this effective field theory reduces to the usual quantum field theory in flat space in the no-gravity limit
Dirac equation in noncommutative space for hydrogen atom

Energy Technology Data Exchange (ETDEWEB)

Adorno, T.C., E-mail: tadorno@nonada.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, CEP 05508-090 Sao Paulo, SP (Brazil); Baldiotti, M.C., E-mail: baldiott@fma.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, CEP 05508-090 Sao Paulo, SP (Brazil); Chaichian, M., E-mail: Masud.Chaichian@helsinki.f [Department of Physics, University of Helsinki and Helsinki Institute of Physics, PO Box 64, FIN-00014 Helsinki (Finland); Gitman, D.M., E-mail: gitman@dfn.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, CEP 05508-090 Sao Paulo, SP (Brazil); Tureanu, A., E-mail: Anca.Tureanu@helsinki.f [Department of Physics, University of Helsinki and Helsinki Institute of Physics, PO Box 64, FIN-00014 Helsinki (Finland)

2009-11-30

We consider the energy levels of a hydrogen-like atom in the framework of theta-modified, due to space noncommutativity, Dirac equation with Coulomb field. It is shown that on the noncommutative (NC) space the degeneracy of the levels 2S{sub 1/2}, 2P{sub 1/2} and 2P{sub 3/2} is lifted completely, such that new transition channels are allowed.
Klein-Gordon oscillators in noncommutative phase space

International Nuclear Information System (INIS)

Wang Jianhua

2008-01-01

We study the Klein-Gordon oscillators in non-commutative (NC) phase space. We find that the Klein-Gordon oscillators in NC space and NC phase-space have a similar behaviour to the dynamics of a particle in commutative space moving in a uniform magnetic field. By solving the Klein-Gordon equation in NC phase space, we obtain the energy levels of the Klein-Gordon oscillators, where the additional terms related to the space-space and momentum-momentum non-commutativity are given explicitly. (authors)
The standard model on non-commutative space-time

International Nuclear Information System (INIS)

Calmet, X.; Jurco, B.; Schupp, P.; Wohlgenannt, M.; Wess, J.

2002-01-01

We consider the standard model on a non-commutative space and expand the action in the non-commutativity parameter θ μν . No new particles are introduced; the structure group is SU(3) x SU(2) x U(1). We derive the leading order action. At zeroth order the action coincides with the ordinary standard model. At leading order in θ μν we find new vertices which are absent in the standard model on commutative space-time. The most striking features are couplings between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity is violated in non-commutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the NCSM to the order considered. (orig.)
Linearization of non-commuting operators in the partition function

International Nuclear Information System (INIS)

Ahmed, M.

1983-06-01

A generalization of the Stratonovich-Hubbard scheme for evaluating the grand canonical partition function is given. The scheme involves linearization of products of non-commuting operators using the functional integral method. The non-commutivity of the operators leads to an additional term which can be absorbed in the single-particle Hamiltonian. (author)
Noncommutative Schur polynomials and the crystal limit of the U_{q} \\widehat{\\mathfrak {sl}}(2)-vertex model

Science.gov (United States)

Korff, Christian

2010-10-01

Starting from the Verma module of U_{q}\\mathfrak {sl}(2) we consider the evaluation module for affine U_{q}\\widehat{\\mathfrak {sl}}(2) and discuss its crystal limit (q → 0). There exists an associated integrable statistical mechanics model on a square lattice defined in terms of vertex configurations. Its transfer matrix is the generating function for noncommutative complete symmetric polynomials in the generators of the affine plactic algebra, an extension of the finite plactic algebra first discussed by Lascoux and Schützenberger. The corresponding noncommutative elementary symmetric polynomials were recently shown to be generated by the transfer matrix of the so-called phase model discussed by Bogoliubov, Izergin and Kitanine. Here we establish that both generating functions satisfy Baxter's TQ-equation in the crystal limit by tying them to special U_{q}\\widehat{ \\mathfrak {sl}}(2) solutions of the Yang-Baxter equation. The TQ-equation amounts to the well-known Jacobi-Trudi formula leading naturally to the definition of noncommutative Schur polynomials. The latter can be employed to define a ring which has applications in conformal field theory and enumerative geometry: it is isomorphic to the fusion ring of the \\widehat{\\mathfrak {sl}}(n)_{k} Wess-Zumino-Novikov-Witten model whose structure constants are the dimensions of spaces of generalized θ-functions over the Riemann sphere with three punctures.
Noncommutative duality of Gelfand-Naimark and applications in gauge theory and spinc structure

International Nuclear Information System (INIS)

RATSIMBARISON, H.M.

2004-01-01

We use the GN (Gelfand-Naimark) duality and its generalizations in order to describe some physical constructions, our main tool is the categorical formalism. We start with the first GN theorem, a duality between a category of commutative unital C*-algebras and a category of compact Hausdorff spaces, which we interpret as equivalence between classical observables and classical states. Then, we give the GNS construction providing the 'Fock space' in Quantum Field Theory, and which is the constructive proof of the second GN theorem. A particular formulation of this latter, the Serre-Swan theorem introduces vector bundle structure, a new kind of classical states space. And this lead to K-theory, which we show compatible with a noncommutative concept : the Morita equivalence. From these ideas of Noncommutative geometry, we meet two important applications in QFT : Gauge theory and Spin c structure.The first application begin with the origin of gauge theory: it permit to obtain the interaction lagrangian term from the gauge non invariance of the free lagrangian of matter. Thanks to theories of principal bundles, the gauge potential and the gauge transformation are represented by connection and bundle G-automorphism on the identity of a principal bundle over the spacetime manifold. Finally, the Serre-Swan theorem gives the step of Connes's generalization to noncommutative case. In the second application, we show that the construction of Dirac operator lead to the definitions of Clifford algebra and spinor space. A categorical equivalent definition, similar to those of the Grothendieck group, is done. At the end, we make use of the structure of Clifford algebra and the Morita equivalence to reconstruct Plymen's definition of the spin c structure [fr

Phase transition and entropy inequality of noncommutative black holes in a new extended phase space

Energy Technology Data Exchange (ETDEWEB)

Miao, Yan-Gang; Xu, Zhen-Ming, E-mail: miaoyg@nankai.edu.cn, E-mail: xuzhenm@mail.nankai.edu.cn [School of Physics, Nankai University, Tianjin 300071 (China)

2017-03-01

We analyze the thermodynamics of the noncommutative high-dimensional Schwarzschild-Tangherlini AdS black hole with the non-Gaussian smeared matter distribution by regarding a noncommutative parameter as an independent thermodynamic variable named as the noncommutative pressure . In the new extended phase space that includes this noncommutative pressure and its conjugate variable, we reveal that the noncommutative pressure and the original thermodynamic pressure related to the negative cosmological constant make the opposite effects in the phase transition of the noncommutative black hole, i.e. the former dominates the UV regime while the latter does the IR regime, respectively. In addition, by means of the reverse isoperimetric inequality, we indicate that only the black hole with the Gaussian smeared matter distribution holds the maximum entropy for a given thermodynamic volume among the noncommutative black holes with various matter distributions.
Baecklund transformation of the noncommutative Gelfand-Dickey hierarchy

International Nuclear Information System (INIS)

Zheng Zhong; He Jingsong; Cheng Yi

2004-01-01

We study the Baecklund transformation of the noncommutative Gelfand-Dickey(ncGD) hierarchy. By factorizing its Lax operator into the multiplication form of first order differential operator, the noncommutative modified KdV(ncMKdV) hierarchy and the Miura transformations are defined. Our results show that the ncMKdV equations are invariant under the cyclic permutation, and hence induces the Baecklund transformation of the ncGD hierarchy. (author)
Can noncommutativity resolve the Big-Bang singularity?

CERN Document Server

Maceda, M; Manousselis, P; Zoupanos, George

2004-01-01

A possible way to resolve the singularities of general relativity is proposed based on the assumption that the description of space-time using commuting coordinates is not valid above a certain fundamental scale. Beyond that scale it is assumed that the space-time has noncommutative structure leading in turn to a resolution of the singularity. As a first attempt towards realizing the above programme a noncommutative version of the Kasner metric is constructed which is nonsingular at all scales and becomes commutative at large length scales.
Principal noncommutative torus bundles

DEFF Research Database (Denmark)

Echterhoff, Siegfried; Nest, Ryszard; Oyono-Oyono, Herve

2008-01-01

of bivariant K-theory (denoted RKK-theory) due to Kasparov. Using earlier results of Echterhoff and Williams, we shall give a complete classification of principal non-commutative torus bundles up to equivariant Morita equivalence. We then study these bundles as topological fibrations (forgetting the group...
Noncommutative gauge theory and symmetry breaking in matrix models

International Nuclear Information System (INIS)

Grosse, Harald; Steinacker, Harold; Lizzi, Fedele

2010-01-01

We show how the fields and particles of the standard model can be naturally realized in noncommutative gauge theory. Starting with a Yang-Mills matrix model in more than four dimensions, an SU(n) gauge theory on a Moyal-Weyl space arises with all matter and fields in the adjoint of the gauge group. We show how this gauge symmetry can be broken spontaneously down to SU(3) c xSU(2) L xU(1) Q [resp. SU(3) c xU(1) Q ], which couples appropriately to all fields in the standard model. An additional U(1) B gauge group arises which is anomalous at low energies, while the trace-U(1) sector is understood in terms of emergent gravity. A number of additional fields arise, which we assume to be massive, in a pattern that is reminiscent of supersymmetry. The symmetry breaking might arise via spontaneously generated fuzzy spheres, in which case the mechanism is similar to brane constructions in string theory.
Open membranes in a constant C-field background and noncommutative boundary strings

International Nuclear Information System (INIS)

Kawamoto, Shoichi; Sasakura, Naoki

2000-01-01

We investigate the dynamics of open membrane boundaries in a constant C-field background. We follow the analysis for open strings in a B-field background, and take some approximations. We find that open membrane boundaries do show noncommutativity in this case by explicit calculations. Membrane boundaries are one dimensional strings, so we face a new type of noncommutativity, that is, noncommutative strings. (author)
The standard model on non-commutative space-time

Energy Technology Data Exchange (ETDEWEB)

Calmet, X.; Jurco, B.; Schupp, P.; Wohlgenannt, M. [Sektion Physik, Universitaet Muenchen (Germany); Wess, J. [Sektion Physik, Universitaet Muenchen (Germany); Max-Planck-Institut fuer Physik, Muenchen (Germany)

2002-03-01

We consider the standard model on a non-commutative space and expand the action in the non-commutativity parameter {theta}{sup {mu}}{sup {nu}}. No new particles are introduced; the structure group is SU(3) x SU(2) x U(1). We derive the leading order action. At zeroth order the action coincides with the ordinary standard model. At leading order in {theta}{sup {mu}}{sup {nu}} we find new vertices which are absent in the standard model on commutative space-time. The most striking features are couplings between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity is violated in non-commutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the NCSM to the order considered. (orig.)
Remarks on the formulation of quantum mechanics on noncommutative phase spaces

International Nuclear Information System (INIS)

Muthukumar, Balasundaram

2007-01-01

We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and also with canonically conjugate momenta. With a postulated normalized distribution function in the quantum domain, the square of the Dirac delta density distribution in the classical case is properly realised in noncommutative phase space and it serves as the quantum condition. With only these inputs, we pull out the entire formalisms of noncommutative quantum mechanics in phase space and in Hilbert space, and elegantly establish the link between classical and quantum formalisms and between Hilbert space and phase space formalisms of noncommutative quantum mechanics. Also, we show that the distribution function in this case possesses 'twisted' Galilean symmetry
The boosts in the noncommutative special relativity

International Nuclear Information System (INIS)

Lagraa, M.

2001-01-01

From the quantum analogue of the Iwasawa decomposition of SL(2, C) group and the correspondence between quantum SL(2, C) and Lorentz groups we deduce the different properties of the Hopf algebra representing the boost of particles in noncommutative special relativity. The representation of the boost in the Hilbert space states is investigated and the addition rules of the velocities are established from the coaction. The q-deformed Clebsch-Gordon coefficients describing the transformed states of the evolution of particles in noncommutative special relativity are introduced and their explicit calculation are given. (author)
Almost-commutative geometries beyond the standard model

International Nuclear Information System (INIS)

Stephan, Christoph A

2006-01-01

In Iochum et al (2004 J. Math. Phys. 45 5003), Jureit and Stephan (2005 J. Math. Phys. 46 043512), Schuecker T (2005 Preprint hep-th/0501181) and Jureit et al (2005 J. Math. Phys. 46 072303), a conjecture is presented that almost-commutative geometries, with respect to sensible physical constraints, allow only the standard model of particle physics and electro-strong models as Yang-Mills-Higgs theories. In this paper, a counter-example will be given. The corresponding almost-commutative geometry leads to a Yang-Mills-Higgs model which consists of the standard model of particle physics and two new fermions of opposite electro-magnetic charge. This is the second Yang-Mills-Higgs model within noncommutative geometry, after the standard model, which could be compatible with experiments. Combined to a hydrogen-like composite particle, these new particles provide a novel dark matter candidate
Worldline approach to noncommutative field theory

International Nuclear Information System (INIS)

Bonezzi, R; Corradini, O; Viñas, S A Franchino; Pisani, P A G

2012-01-01

The study of the heat-trace expansion in non-commutative field theory has shown the existence of Moyal non-local Seeley–DeWitt coefficients which are related to the UV/IR mixing and manifest, in some cases, the non-renormalizability of the theory. We show that these models can be studied in a worldline approach implemented in phase space and arrive at a master formula for the n-point contribution to the heat-trace expansion. This formulation could be useful in understanding some open problems in this area, as the heat-trace expansion for the non-commutative torus or the introduction of renormalizing terms in the action, as well as for generalizations to other non-local operators. (paper)
On a direct approach to quasideterminant solutions of a noncommutative modified KP equation

International Nuclear Information System (INIS)

Gilson, C R; Nimmo, J J C; Sooman, C M

2008-01-01

A noncommutative version of the modified KP equation and a family of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means of Darboux transformations and the solutions are verified directly. We also verify directly an explicit connection between quasideterminant solutions of the noncommutative mKP equation and the noncommutative KP equation arising from the Miura transformation
Hydrogen atom spectrum and the Lamb shift in noncommutative QED

International Nuclear Information System (INIS)

Chaichian, M. . Helsinki Institute of Physics, Helsinki; Tureanu, A. . Helsinki Institute of Physics, Helsinki; FI)

2000-10-01

We have calculated the energy levels of the hydrogen atom and as well the Lamb shift within the noncommutative quantum electrodynamics theory. The results show deviations from the usual QED both on the classical and on the quantum levels. On both levels, the deviations depend on the parameter of space/space noncommutativity. (author)
Dirac-Kahler fermion with noncommutative differential forms on a lattice

International Nuclear Information System (INIS)

Kanamori, I.; Kawamoto, N.

2004-01-01

Noncommutativity between a differential form and a function allows us to define differential operator satisfying Leibniz's rule on a lattice. We propose a new associative Clifford product defined on the lattice by introducing the noncommutative differential forms. We show that this Clifford product naturally leads to the Dirac-Kaehler fermion on the lattice
Noncommutative instantons: a new approach

International Nuclear Information System (INIS)

Schwarz, A.

2001-01-01

We discuss instantons on noncommutative four-dimensional Euclidean space. In the commutative case one can consider instantons directly on Euclidean space, then we should restrict ourselves to the gauge fields that are gauge equivalent to the trivial field at infinity. However, technically it is more convenient to work on the four-dimensional sphere. We will show that the situation in the noncommutative case is quite similar. One can analyze instantons taking as a starting point the algebra of smooth functions vanishing at infinity, but it is convenient to add a unit element to this algebra (this corresponds to a transition to a sphere at the level of topology). Our approach is more rigorous than previous considerations; it seems that it is also simpler and more transparent. In particular, we obtain the ADHM equations in a very simple way. (orig.)
Non-commutative covering spaces and their symmetries

DEFF Research Database (Denmark)

Canlubo, Clarisson

dened and its corresponding Galois theory. Using this and basic concepts from algebraic geometryand spectral theory, we will give a full description of the general structure of non-centralcoverings. Examples of coverings of the rational and irrational non-commutative tori will alsobe studied. Using...... will explain this and relate it to bi-Galois theory.Using the OZ-transform, we will show that non-commutative covering spaces come in pairs.Several categories of covering spaces will be dened and studied. Appealing to Tannaka duality,we will explain how this lead to a notion of an etale fundamental group...
PURE STATE ENTANGLEMENT ENTROPY IN NONCOMMUTATIVE 2D DE SITTER SPACE TIME

Directory of Open Access Journals (Sweden)

M.F Ghiti

2014-12-01

Full Text Available Using the general modified field equation, a general noncommutative Klein-Gordon equation up to the second order of the noncommutativity parameter is derived in the context of noncommutative 2D De Sitter space-time. Using Bogoliubov coefficients and a special technics called conformal time; the boson-antiboson pair creation density is determined. The Von Neumann boson-antiboson pair creation quantum entanglement entropy is presented to compute the entanglement between the modes created presented.
On the energy crisis in noncommutative CP(1) model

International Nuclear Information System (INIS)

Sourrouille, Lucas

2010-01-01

We study the CP(1) system in (2+1)-dimensional noncommutative space with and without Chern-Simons term. Using the Seiberg-Witten map we convert the noncommutative CP(1) system to an action written in terms of the commutative fields. We find that this system presents the same infinite size instanton solution as the commutative Chern-Simons-CP(1) model without a potential term. Based on this result we argue that the BPS equations are compatible with the full variational equations of motion, rejecting the hypothesis of an 'energy crisis'. In addition we examine the noncommutative CP(1) system with a Chern-Simons interaction. In this case we find that when the theory is transformed by the Seiberg-Witten map it also presents the same instanton solution as the commutative Chern-Simons-CP(1) model.
Seiberg–Witten map and quantum phase effects for neutral Dirac particle on noncommutative plane

Directory of Open Access Journals (Sweden)

Kai Ma

2016-05-01

Full Text Available We provide a new approach to study the noncommutative effects on the neutral Dirac particle with anomalous magnetic or electric dipole moment on the noncommutative plane. The advantages of this approach are demonstrated by investigating the noncommutative corrections on the Aharonov–Casher and He–McKellar–Wilkens effects. This approach is based on the effective U(1 gauge symmetry for the electrodynamics of spin on the two dimensional space. The Seiberg–Witten map for this symmetry is then employed when we study the noncommutative corrections. Because the Seiberg–Witten map preserves the gauge symmetry, the noncommutative corrections can be defined consistently with the ordinary phases. Based on this approach we find the noncommutative corrections on the Aharonov–Casher and He–McKellar–Wilkens phases consist of two terms. The first one depends on the beam particle velocity and consistence with the previous results. However the second term is velocity-independent and then completely new. Therefore our results indicate it is possible to investigate the noncommutative space by using ultra-cold neutron interferometer in which the velocity-dependent term is negligible. Furthermore, both these two terms are proportional to the ratio between the noncommutative parameter θ and the cross section Ae/m of the electrical/magnetic charged line enclosed by the trajectory of beam particles. Therefore the experimental sensitivity can be significantly enhanced by reducing the cross section of the charge line Ae/m.
Quantum κ-deformed differential geometry and field theory

Science.gov (United States)

Mercati, Flavio

2016-03-01

I introduce in κ-Minkowski noncommutative spacetime the basic tools of quantum differential geometry, namely bicovariant differential calculus, Lie and inner derivatives, the integral, the Hodge-∗ and the metric. I show the relevance of these tools for field theory with an application to complex scalar field, for which I am able to identify a vector-valued four-form which generalizes the energy-momentum tensor. Its closedness is proved, expressing in a covariant form the conservation of energy-momentum.

Supergravity couplings to Noncommutative Branes, Open Wilson Lines and Generalised Star Products

International Nuclear Information System (INIS)

Das, S.R.; Trivedi, S.P.

2001-01-01

Noncommutative gauge theories can be constructed from ordinary U(∞) gauge theories in lower dimensions. Using this construction we identify the operators on noncommutative D-branes which couple to linearized supergravity backgrounds, from a knowledge of such couplings to lower dimensional D-branes with no B field. These operators belong to a class of gauge invariant observables involving open Wilson lines. Assuming a DBI form of the coupling we show, to second order in the gauge potential but to all orders of the noncommutativity parameter, that our proposal agrees with the operator obtained in terms of ordinary gauge fields by considering brane actions in backgrounds and then using the Seiberg-Witten map to rewrite this in terms of noncommutative gauge fields. Our result clarify why a certain commutative but non-associative 'generalized star product' appears both in the expansion of the open Wilson line, as well as in string amplitude computations of open string-closed string couplings. We outline how our procedure can be used to obtain operators in the noncommutative theory which are holographically dual to supergravity modes. (author)
On the generalization of linear least mean squares estimation to quantum systems with non-commutative outputs

Energy Technology Data Exchange (ETDEWEB)

Amini, Nina H. [Stanford University, Edward L. Ginzton Laboratory, Stanford, CA (United States); CNRS, Laboratoire des Signaux et Systemes (L2S) CentraleSupelec, Gif-sur-Yvette (France); Miao, Zibo; Pan, Yu; James, Matthew R. [Australian National University, ARC Centre for Quantum Computation and Communication Technology, Research School of Engineering, Canberra, ACT (Australia); Mabuchi, Hideo [Stanford University, Edward L. Ginzton Laboratory, Stanford, CA (United States)

2015-12-15

The purpose of this paper is to study the problem of generalizing the Belavkin-Kalman filter to the case where the classical measurement signal is replaced by a fully quantum non-commutative output signal. We formulate a least mean squares estimation problem that involves a non-commutative system as the filter processing the non-commutative output signal. We solve this estimation problem within the framework of non-commutative probability. Also, we find the necessary and sufficient conditions which make these non-commutative estimators physically realizable. These conditions are restrictive in practice. (orig.)
Conference on Strings, Duality, and Geometry

CERN Document Server

Phong, Duong; Yau, Shing-Tung; Mirror Symmetry IV

2002-01-01

This book presents contributions of participants of a workshop held at the Centre de Recherches Mathématiques (CRM), University of Montréal. It can be viewed as a sequel to Mirror Symmetry I (1998), Mirror Symmetry II (1996), and Mirror Symmetry III (1999), copublished by the AMS and International Press. The volume presents a broad survey of many of the noteworthy developments that have taken place in string theory, geometry, and duality since the mid 1990s. Some of the topics emphasized include the following: Integrable models and supersymmetric gauge theories; theory of M- and D-branes and noncommutative geometry; duality between strings and gauge theories; and elliptic genera and automorphic forms. Several introductory articles present an overview of the geometric and physical aspects of mirror symmetry and of corresponding developments in symplectic geometry. The book provides an efficient way for a very broad audience of mathematicians and physicists to explore the frontiers of research into this rapi...
Gauge theories of gravity

International Nuclear Information System (INIS)

Ne'eman, Y.

1998-01-01

The relatively simple Fibre-Bundle geometry of a Yang-Mills gauge theory - mainly the clear distinction between base and fibre - made it possible, between 1953 and 1971, to construct a fully quantized version and prove that theory's renormalizability; moreover, nonperturbative (topological) solutions were subsequently found in both the fully symmetric and the spontaneously broken modes (instantons, monopoles). Though originally constructed as a model formalism, it became in 1974 the mathematical mold holding the entire Standard Model (i.e. QCD and the Electroweak theory). On the other hand, between 1974 and 1984, Einstein's theory was shown to be perturbatively nonrenormalizable. Since 1974, the search for Quantum Gravity has therefore provided the main motivation for the construction of Gauge Theories of Gravity. Earlier, however, in 1958-76 several such attempts were initiated, for aesthetic or heuristic reasons, to provide a better understanding of the algebraic structure of GR. A third motivation has come from the interest in Unification, making it necessary to bring GR into a form compatible with an enlargement of the Standard Model. Models can be classified according to the relevant structure group in the fibre. Within the Poincare group, this has been either the R 4 translations, or the Lorentz group SL(2, C) - or the entire Poincare SL(2, C) x R 4 . Enlarging the group has involved the use of the Conformal SU(2, 2), the special Affine SA(4, R) = SL(4, R) x R 4 or Affine A(4, R) groups. Supergroups have included supersymmetry, i.e. the graded-Poincare group (n =1...8 m its extensions) or the superconformal SU(2, 2/n). These supergravity theories have exploited the lessons of the aesthetic-heuristic models - Einstein-Cartan etc. - and also achieved the Unification target. Although perturbative renormalizability has been achieved in some models, whether they satisfy unitarity is not known. The nonperturbative Ashtekar program has exploited the understanding of
Chiral topological insulator on Nambu 3-algebraic geometry

Directory of Open Access Journals (Sweden)

Kazuki Hasebe

2014-09-01

Full Text Available Chiral topological insulator (AIII-class with Landau levels is constructed based on the Nambu 3-algebraic geometry. We clarify the geometric origin of the chiral symmetry of the AIII-class topological insulator in the context of non-commutative geometry of 4D quantum Hall effect. The many-body groundstate wavefunction is explicitly derived as a (l,l,l−1 Laughlin–Halperin type wavefunction with unique K-matrix structure. Fundamental excitation is identified with anyonic string-like object with fractional charge 1/(2(l−12+1. The Hall effect of the chiral topological insulators turns out be a color version of Hall effect, which exhibits a dual property of the Hall and spin-Hall effects.
Statistical mechanics of free particles on space with Lie-type noncommutativity

Energy Technology Data Exchange (ETDEWEB)

Shariati, Ahmad; Khorrami, Mohammad; Fatollahi, Amir H, E-mail: shariati@mailaps.or, E-mail: mamwad@mailaps.or, E-mail: ahfatol@gmail.co [Department of Physics, Alzahra University, Tehran 1993891167 (Iran, Islamic Republic of)

2010-07-16

Effects of Lie-type noncommutativity on thermodynamic properties of a system of free identical particles are investigated. A definition for finite volume of the configuration space is given, and the grandcanonical partition function in the thermodynamic limit is calculated. Two possible definitions for the pressure are discussed, which are equivalent when the noncommutativity vanishes. The thermodynamic observables are extracted from the partition function. Different limits are discussed where either the noncommutativity or the quantum effects are important. Finally, specific cases are discussed where the group is SU(2) or SO(3), and the partition function of a nondegenerate gas is calculated.
Connecting dissipation and noncommutativity: A Bateman system case study

Science.gov (United States)

Pal, Sayan Kumar; Nandi, Partha; Chakraborty, Biswajit

2018-06-01

We present an approach to the problem of quantization of the damped harmonic oscillator. To start with, we adopt the standard method of doubling the degrees of freedom of the system (Bateman form) and then, by introducing some new parameters, we get a generalized coupled set of equations from the Bateman form. Using the corresponding time-independent Lagrangian, quantum effects on a pair of Bateman oscillators embedded in an ambient noncommutative space (Moyal plane) are analyzed by using both path integral and canonical quantization schemes within the framework of the Hilbert-Schmidt operator formulation. Our method is distinct from those existing in the literature and where the ambient space was taken to be commutative. Our quantization shows that we end up again with a Bateman system except that the damping factor undergoes renormalization. Strikingly, the corresponding expression shows that the renormalized damping factor can be nonzero even if "bare" one is zero to begin with. In other words, noncommutativity can act as a source of dissipation. Conversely, the noncommutative parameter θ , taken to be a free one now, can be fine tuned to get a vanishing renormalized damping factor. This indicates in some sense a "duality" between dissipation and noncommutativity. Our results match the existing results in the commutative limit.
Noncommutative field theory

International Nuclear Information System (INIS)

Douglas, Michael R.; Nekrasov, Nikita A.

2001-01-01

This article reviews the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, on both the classical and the quantum level
Pair production of Dirac particles in a d + 1-dimensional noncommutative space-time

Energy Technology Data Exchange (ETDEWEB)

Ousmane Samary, Dine [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin); N' Dolo, Emanonfi Elias; Hounkonnou, Mahouton Norbert [University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin)

2014-11-15

This work addresses the computation of the probability of fermionic particle pair production in d + 1-dimensional noncommutative Moyal space. Using Seiberg-Witten maps, which establish relations between noncommutative and commutative field variables, up to the first order in the noncommutative parameter θ, we derive the probability density of vacuum-vacuum pair production of Dirac particles. The cases of constant electromagnetic, alternating time-dependent, and space-dependent electric fields are considered and discussed. (orig.)
Gravity and strings

CERN Document Server

Ortín, Tomás

2015-01-01

Self-contained and comprehensive, this definitive new edition of Gravity and Strings is a unique resource for graduate students and researchers in theoretical physics. From basic differential geometry through to the construction and study of black-hole and black-brane solutions in quantum gravity - via all the intermediate stages - this book provides a complete overview of the intersection of gravity, supergravity, and superstrings. Now fully revised, this second edition covers an extensive array of topics, including new material on non-linear electric-magnetic duality, the electric-tensor formalism, matter-coupled supergravity, supersymmetric solutions, the geometries of scalar manifolds appearing in 4- and 5-dimensional supergravities, and much more. Covering reviews of important solutions and numerous solution-generating techniques, and accompanied by an exhaustive index and bibliography, this is an exceptional reference work.
Noncommutativity into Dirac Equation with mass dependent on the position

International Nuclear Information System (INIS)

Bastos, Samuel Batista; Almeida, Carlos Alberto Santos; Nunes, Luciana Angelica da Silva

2013-01-01

Full text: In recent years, there is growing interest in the study of theories in non-commutative spaces. Non-commutative fields theories are related with compactifications of M theory, string theory and the quantum Hall effect. Moreover, the role of the non-commutativity of theories of a particle finds large applications when analyzed in scenarios of quantum mechanics and relativistic quantum mechanics. In these contexts investigations on the Schrodinger and Dirac equations with mass depending on the position (MDP) has attracted much attention in the literature. Systems endowed with MDP models are useful for the study of many physical problems. In particular, they are used to study the energy density in problems of many bodies, determining the electronic properties of semiconductor heterostructures and also to describe the properties of heterojunctions and quantum dots. In particular, the investigation of relativistic effects it is important for systems containing heavy atoms or doping by heavy ions. For these types of materials, the study of the properties of the Dirac equation, in the case where the mass becomes variable is of great interest. In this paper, we seek for the non-relativistic limit of the Dirac Hamiltonian in the context of a theory of effective mass, through a Foldy-Wouthuysen transformation. We analyse the Dirac equation with mass dependent on the position, in a smooth step shape mass distribution, in non-commutative space (NC). This potential type kink was recently discussed by several authors in the commutative context and now we present our results in the non-commutative context. (author)
Noncommuting observables and local realism

International Nuclear Information System (INIS)

Malley, James D.; Fine, Arthur

2005-01-01

A standard approach in the foundations of quantum mechanics studies local realism and hidden variables models exclusively in terms of violations of Bell-like inequalities. Thus quantum nonlocality is tied to the celebrated no-go theorems, and these comprise a long list that includes the Kochen-Specker and Bell theorems, as well as elegant refinements by Mermin, Peres, Hardy, GHZ, and many others. Typically entanglement or carefully prepared multipartite systems have been considered essential for violations of local realism and for understanding quantum nonlocality. Here we show, to the contrary, that sharp violations of local realism arise almost everywhere without entanglement. The pivotal fact driving these violations is just the noncommutativity of quantum observables. We demonstrate how violations of local realism occur for arbitrary noncommuting projectors, and for arbitrary quantum pure states. Finally, we point to elementary tests for local realism, using single particles and without reference to entanglement, thus avoiding experimental loopholes and efficiency issues that continue to bedevil the Bell inequality related tests
Strings from position-dependent noncommutativity

International Nuclear Information System (INIS)

Fring, Andreas; Gouba, Laure; Scholtz, Frederik G

2010-01-01

We introduce a new set of noncommutative spacetime commutation relations in two space dimensions. The space-space commutation relations are deformations of the standard flat noncommutative spacetime relations taken here to have position-dependent structure constants. Some of the new variables are non-Hermitian in the most natural choice. We construct their Hermitian counterparts by means of a Dyson map, which also serves to introduce a new metric operator. We propose PT-like symmetries, i.e. antilinear involutory maps, respected by these deformations. We compute minimal lengths and momenta arising in this space from generalized versions of Heisenberg's uncertainty relations and find that any object in this two-dimensional space is string like, i.e. having a fundamental length in one direction beyond which a resolution is impossible. Subsequently, we formulate and partly solve some simple models in these new variables, the free particle, its PT-symmetric deformations and the harmonic oscillator.
Light-like noncommutativity, light-front quantization and new light on UV/IR mixing

International Nuclear Information System (INIS)

Sheikh-Jabbari, M.M.; Tureanu, A.

2011-01-01

We revisit the problem of quantizing field theories on noncommutative Moyal space-time with light-like noncommutativity. To tackle the issues arising from noncommuting and hence nonlocal time, we argue that for this case light-front quantization procedure should be employed. In this appropriate quantization scheme we perform the non-planar loop analysis for the light-like noncommutative field theories. One of the important and peculiar features of light-front quantization is that the UV cutoff of the light-cone Hamiltonian manifests itself as an IR cutoff for the light-cone momentum, p + . Due to this feature, the naive results of covariant quantization for the light-like case allude to the absence of the UV/IR mixing in the light-front quantization. However, by a careful analysis of non-planar loop integrals we show that this is not the case and the UV/IR mixing persists. In addition, we argue in favour of the perturbative unitarity of light-like noncommutative field theories in the light-front quantization scheme.
Non-commutative Nash inequalities

International Nuclear Information System (INIS)

Kastoryano, Michael; Temme, Kristan

2016-01-01

A set of functional inequalities—called Nash inequalities—are introduced and analyzed in the context of quantum Markov process mixing. The basic theory of Nash inequalities is extended to the setting of non-commutative L p spaces, where their relationship to Poincaré and log-Sobolev inequalities is fleshed out. We prove Nash inequalities for a number of unital reversible semigroups
Closed star product on noncommutative ℝ{sup 3} and scalar field dynamics

Energy Technology Data Exchange (ETDEWEB)

Jurić, Tajron [Ruđer Bošković Institute, Theoretical Physics Division,Bijenička c. 54, HR-10002 Zagreb (Croatia); Poulain, Timothé; Wallet, Jean-Christophe [Laboratoire de Physique Théorique, CNRS,University of Paris-Sud, University of Paris-Saclay,Bât. 210, 91405 Orsay (France)

2016-05-25

We consider the noncommutative space ℝ{sub θ}{sup 3}, a deformation of ℝ{sup 3} for which the star product is closed for the trace functional. We study one-loop IR and UV properties of the 2-point function for real and complex noncommutative scalar field theories with quartic interactions and Laplacian on ℝ{sup 3} as kinetic operator. We find that the 2-point functions for these noncommutative scalar field theories have no IR singularities in the external momenta, indicating the absence of UV/IR mixing. We also find that the 2-point functions are UV finite with the deformation parameter θ playing the role of a natural UV cut-off. The possible origin of the absence of UV/IR mixing in noncommutative scalar field theories on ℝ{sub θ}{sup 3} as well as on ℝ{sub λ}{sup 3}, another deformation of ℝ{sup 3}, is discussed.
Quantum effects of Aharonov-Bohm type and noncommutative quantum mechanics

Science.gov (United States)

Rodriguez R., Miguel E.

2018-01-01

Quantum mechanics in noncommutative space modifies the standard result of the Aharonov-Bohm effect for electrons and other recent quantum effects. Here we obtain the phase in noncommutative space for the Spavieri effect, a generalization of Aharonov-Bohm effect which involves a coherent superposition of particles with opposite charges moving along a single open interferometric path. By means of the experimental considerations a limit √{θ }≃(0.13TeV)-1 is achieved, improving by 10 orders of magnitude the results derived by Chaichian et al. [Phys. Lett. B 527, 149 (2002), 10.1016/S0370-2693(02)01176-0] for the Aharonov-Bohm effect. It is also shown that the noncommutative phases of the Aharonov-Casher and He-McKellar-Willkens effects are nullified in the current experimental tests.
Relativistic Equations for Spin Particles: What can We Learn from Noncommutativity?

International Nuclear Information System (INIS)

Dvoeglazov, V. V.

2009-01-01

We derive relativistic equations for charged and neutral spin particles. The approach for higher-spin particles is based on generalizations of the Bargmann-Wigner formalism. Next, we study, what new physical information can give the introduction of non-commutativity. Additional non-commutative parameters can provide a suitable basis for explanation of the origin of mass.
Noether analysis of the twisted Hopf symmetries of canonical noncommutative spacetimes

International Nuclear Information System (INIS)

Amelino-Camelia, Giovanni; Gubitosi, Giulia; Marciano, Antonino; Martinetti, Pierre; Mercati, Flavio; Briscese, Fabio

2008-01-01

We study the twisted Hopf-algebra symmetries of observer-independent canonical spacetime noncommutativity, for which the commutators of the spacetime coordinates take the form [x^ μ ,x^ ν ]=iθ μν with observer-independent (and coordinate-independent) θ μν . We find that it is necessary to introduce nontrivial commutators between transformation parameters and spacetime coordinates, and that the form of these commutators implies that all symmetry transformations must include a translation component. We show that with our noncommutative transformation parameters the Noether analysis of the symmetries is straightforward, and we compare our canonical-noncommutativity results with the structure of the conserved charges and the ''no-pure-boost'' requirement derived in a previous study of κ-Minkowski noncommutativity. We also verify that, while at intermediate stages of the analysis we do find terms that depend on the ordering convention adopted in setting up the Weyl map, the final result for the conserved charges is reassuringly independent of the choice of Weyl map and (the corresponding choice of) star product.
Deformed special relativity as an effective flat limit of quantum gravity

International Nuclear Information System (INIS)

Girelli, Florian; Livine, Etera R.; Oriti, Daniele

2005-01-01

We argue that a (slightly) curved space-time probed with a finite resolution, equivalently a finite minimal length, is effectively described by a flat non-commutative space-time. More precisely, a small cosmological constant (so a constant curvature) leads the κ-deformed Poincare flat space-time of deformed special relativity (DSR) theories. This point of view eventually helps understanding some puzzling features of DSR. It also explains how DSR can be considered as an effective flat (low energy) limit of a (true) quantum gravity theory. This point of view leads us to consider a possible generalization of DSR to arbitrary curvature in momentum space and to speculate about a possible formulation of an effective quantum gravity model in these terms. It also leads us to suggest a doubly deformed special relativity framework for describing particle kinematics in an effective low energy description of quantum gravity

The noncommutative standard model. Construction beyond leading order in θ and collider phenomenology

International Nuclear Information System (INIS)

Alboteanu, A.M.

2007-01-01

Within this work we study the phenomenological consequences of a possible realization of QFT on noncommutative space-time. In the first part we performed a phenomenological analysis of the hadronic process pp → Z γ → l + l - γ at the LHC and of electron-positron pair annihilation into a Z boson and a photon at the International Linear Collider (ILC). The noncommutative extension of the SM considered within this work relies on two building blocks: the Moyal-Weyl *-product of functions on ordinary space-time and the Seiberg-Witten maps. A consequence of the noncommutativity of space-time is the violation of rotational invariance with respect to the beam axis. This effect shows up in the azimuthal dependence of cross sections, which is absent in the SM as well as in other models beyond the SM. We have found this dependence to be best suited for deriving the sensitivity bounds on the noncommutative scale NC. By studying pp→Z γ →l + l - γ to first order in the noncommutative parameter θ, we show in the first part of this work that measurements at the LHC are sensitive to noncommutative effects only in certain cases, giving bounds on the noncommutative scale of Λ NC >or similar 1.2 TeV. By means of e + e - → Z γ → l + l - γ to O(θ) we have shown that ILC measurements are complementary to LHC measurements of the noncommutative parameters. In addition, the bounds on Λ NC derived from the ILC are significantly higher and reach Λ NC >or similar 6 TeV. In the second part of this work we expand the neutral current sector of the noncommutative SM to second order in θ. We found that, against the general expectation, the theory must be enlarged by additional parameters. The new parameters enter the theory as ambiguities of the Seiberg-Witten maps. The latter are not uniquely determined and differ by homogeneous solutions of the gauge equivalence equations. The expectation was that the ambiguities correspond to field redefinitions and therefore should
The noncommutative standard model. Construction beyond leading order in {theta} and collider phenomenology

Energy Technology Data Exchange (ETDEWEB)

Alboteanu, A.M.

2007-07-01

Within this work we study the phenomenological consequences of a possible realization of QFT on noncommutative space-time. In the first part we performed a phenomenological analysis of the hadronic process pp {yields} Z{sub {gamma}} {yields} l{sup +}l{sup -}{gamma} at the LHC and of electron-positron pair annihilation into a Z boson and a photon at the International Linear Collider (ILC). The noncommutative extension of the SM considered within this work relies on two building blocks: the Moyal-Weyl *-product of functions on ordinary space-time and the Seiberg-Witten maps. A consequence of the noncommutativity of space-time is the violation of rotational invariance with respect to the beam axis. This effect shows up in the azimuthal dependence of cross sections, which is absent in the SM as well as in other models beyond the SM. We have found this dependence to be best suited for deriving the sensitivity bounds on the noncommutative scale NC. By studying pp{yields}Z{sub {gamma}} {yields}l{sup +}l{sup -}{gamma} to first order in the noncommutative parameter {theta}, we show in the first part of this work that measurements at the LHC are sensitive to noncommutative effects only in certain cases, giving bounds on the noncommutative scale of {lambda}{sub NC} >or similar 1.2 TeV. By means of e{sup +}e{sup -} {yields} Z{sub {gamma}} {yields} l{sup +}l{sup -}{gamma} to O({theta}) we have shown that ILC measurements are complementary to LHC measurements of the noncommutative parameters. In addition, the bounds on {lambda}{sub NC} derived from the ILC are significantly higher and reach {lambda}{sub NC} >or similar 6 TeV. In the second part of this work we expand the neutral current sector of the noncommutative SM to second order in {theta}. We found that, against the general expectation, the theory must be enlarged by additional parameters. The new parameters enter the theory as ambiguities of the Seiberg-Witten maps. The latter are not uniquely determined and differ by
One-loop beta functions for the orientable non-commutative Gross Neveu model TH1"-->

Science.gov (United States)

Lakhoua, A.; Vignes-Tourneret, F.; Wallet, J.-C.

2007-11-01

We compute at the one-loop order the β-functions for a renormalisable non-commutative analog of the Gross Neveu model defined on the Moyal plane. The calculation is performed within the so called x-space formalism. We find that this non-commutative field theory exhibits asymptotic freedom for any number of colors. The β-function for the non-commutative counterpart of the Thirring model is found to be non vanishing.
Dynamics of Strings in Noncommutative Gauge Theory

International Nuclear Information System (INIS)

Gross, David J.; Nekrasov, Nikia A.

2000-01-01

We continue our study of solitons in noncommutative gauge theories and present an extremely simple BPS solution of N=4 U(1) noncommutative gauge theory in 4 dimensions, which describes N infinite D1 strings that pierce a D3 brane at various points, in the presence of a background B-field in the Seiberg-Witten limit. We call this solution the N-fluxon. For N=1 we calculate the complete spectrum of small fluctuations about the fluxon and find three kinds of modes: the fluctuations of the superstring in 10 dimensions arising from fundamental strings attached to the D1 strings, the ordinary particles of the gauge theory in 4 dimensions and a set of states with discrete spectrum, localized at the intersection point - corresponding to fundamental strings stretched between the D1 string and the D3 brane. We discuss the fluctuations about the N-fluxon as well and derive explicit expressions for the amplitudes of interactions between these various modes. We show that translations in noncommutative gauge theories are equivalent to gauge transformations (plus a constant shift of the gauge field) and discuss the implications for the translational zeromodes of our solitons. We also find the dyonic versions of N-fluxon, as well as of our previous string-monopole solution. (author)
Discrete quantum geometries and their effective dimension

International Nuclear Information System (INIS)

Thuerigen, Johannes

2015-01-01

In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then how the smooth geometries of general relativity, expressed in terms of suitable geometric observables, arise from such discrete quantum geometries in some semiclassical and continuum limit. In this thesis I tackle the question of suitable observables focusing on the effective dimension of discrete quantum geometries. For this purpose I give a purely combinatorial description of the discrete structures which these geometries have support on. As a side topic, this allows to present an extension of group field theory to cover the combinatorially larger kinematical state space of loop quantum gravity. Moreover, I introduce a discrete calculus for fields on such fundamentally discrete geometries with a particular focus on the Laplacian. This permits to define the effective-dimension observables for quantum geometries. Analysing various classes of quantum geometries, I find as a general result that the spectral dimension is more sensitive to the underlying combinatorial structure than to the details of the additional geometric data thereon. Semiclassical states in loop quantum gravity approximate the classical geometries they are peaking on rather well and there are no indications for stronger quantum effects. On the other hand, in the context of a more general model of states which are superposition over a large number of complexes, based on analytic solutions, there is a flow of the spectral dimension from the topological dimension d on low energy scales to a real number between 0 and d on high energy scales. In the particular case of 1 these results allow to understand the quantum geometry as effectively fractal.
Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories

International Nuclear Information System (INIS)

Sasai, Yuya; Sasakura, Naoki

2008-01-01

Domain wall solitons are the simplest topological objects in field theories. The conventional translational symmetry in a field theory is the generator of a one-parameter family of domain wall solutions, and induces a massless moduli field which propagates along a domain wall. We study similar issues in braided noncommutative field theories possessing Hopf algebraic translational symmetries. As a concrete example, we discuss a domain wall soliton in the scalar φ 4 braided noncommutative field theory in Lie-algebraic noncommutative space-time, [x i ,x j ]=2iκε ijk x k (i,j,k=1,2,3), which has a Hopf algebraic translational symmetry. We first discuss the existence of a domain wall soliton in view of Derrick's theorem, and construct explicitly a one-parameter family of solutions in perturbation of the noncommutativity parameter κ. We then find the massless moduli field which propagates on the domain wall soliton. We further extend our analysis to the general Hopf algebraic translational symmetry
The Other Side of Gravity and Geometry: Antigravity and Anticurvature

Directory of Open Access Journals (Sweden)

M. I. Wanas

2012-01-01

Full Text Available Gravity is one of the four known fundamental interactions used to study and interpret physical phenomenae. It governs diverse phenomenae, especially those connected with large-scale structures. From more than one decade, existing gravity theories have suffered from some problems, when confronting their predictions with the results of some experiments and observations. This situation has led to many suggestions, none of which is final, so far. Here, we show that the assumption of existence of another side of gravity, a repulsive gravity or antigravity, together with its attractive side, may give a satisfactory solution to gravity problems. We caught here two pieces of evidence for the existence of antigravity in nature. The first is on the laboratory scale, the COW experiment, and the second is on the cosmic scale, SN type Ia observation. On the other hand, we show how gravity theories can predict antigravity, using a new defined geometric object called Parameterized anticurvature. This shows clearly how Einstein's geometrization philosophy can solve recent gravity problems in a satisfactory and easy way. Also, it may throw some light on the mystery of physical nature of “Dark Energy.”
Unruly topologies in two-dimensional quantum gravity

International Nuclear Information System (INIS)

Hartle, J.B.

1985-01-01

A sum over histories formulation of quantum geometry could involve sums over different topologies as well as sums over different metrics. In classical gravity a geometry is a manifold with a metric, but it is difficult to implement a sum over manifolds in quantum gravity. In this difficulty, motivation is found for including in the sum over histories, geometries defined on more general objects than manifolds-unruly topologies. In simplicial two-dimensional quantum gravity a class of simplicial complexes is found to which the gravitational action can be extended, for which sums over the class are straightforwardly defined, and for which a manifold dominates the sum in the classical limit. The situation in higher dimensions is discussed. (author)
Noncommutative o*(N) and usp*(2N) algebras and the corresponding gauge field theories

International Nuclear Information System (INIS)

Bars, I.; Sheikh-Jabbari, M.M.; Vasiliev, M.A.

2001-03-01

The extension of the noncommutative u * (N) Lie algebra to noncommutative orthogonal and symplectic Lie algebras is studied. Using an anti-automorphism of the star-matrix algebra, we show that the u * (N) can consistently be restricted to o * (N) and usp * (N) algebras that have new mathematical structures. We give explicit fundamental matrix representations of these algebras, through which the formulation for the corresponding noncommutative gauge field theories are obtained. In addition, we present a D-brane configuration with an orientifold which realizes geometrically our algebraic construction, thus embedding the new noncommutative gauge theories in superstring theory in the presence of a constant background magnetic field. Some algebraic generalizations that may have applications in other areas of physics are also discussed. (author)
Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry

International Nuclear Information System (INIS)

Alvarez, Pedro D.; Gomis, Joaquim; Kamimura, Kiyoshi; Plyushchay, Mikhail S.

2008-01-01

We investigate the planar anisotropic harmonic oscillator with explicit rotational symmetry as a particle model with non-commutative coordinates. It includes the exotic Newton-Hooke particle and the non-commutative Landau problem as special, isotropic and maximally anisotropic, cases. The system is described by the same (2+1)-dimensional exotic Newton-Hooke symmetry as in the isotropic case, and develops three different phases depending on the values of the two central charges. The special cases of the exotic Newton-Hooke particle and non-commutative Landau problem are shown to be characterized by additional, so(3) or so(2,1) Lie symmetry, which reflects their peculiar spectral properties
Relativistic Hydrogen-Like Atom on a Noncommutative Phase Space

Science.gov (United States)

Masum, Huseyin; Dulat, Sayipjamal; Tohti, Mutallip

2017-09-01

The energy levels of hydrogen-like atom on a noncommutative phase space were studied in the framework of relativistic quantum mechanics. The leading order corrections to energy levels 2 S 1/2, 2 P 1/2 and 2 P 3/2 were obtained by using the 𝜃 and the \\bar θ modified Dirac Hamiltonian of hydrogen-like atom on a noncommutative phase space. The degeneracy of the energy levels 2 P 1/2 and 2 P 3/2 were removed completely by 𝜃-correction. And the \\bar θ -correction shifts these energy levels.
Non-commutative phase space and its space-time symmetry

International Nuclear Information System (INIS)

Li Kang; Dulat Sayipjamal

2010-01-01

First a description of 2+1 dimensional non-commutative (NC) phase space is presented, and then we find that in this formulation the generalized Bopp's shift has a symmetric representation and one can easily and straightforwardly define the star product on NC phase space. Then we define non-commutative Lorentz transformations both on NC space and NC phase space. We also discuss the Poincare symmetry. Finally we point out that our NC phase space formulation and the NC Lorentz transformations are applicable to any even dimensional NC space and NC phase space. (authors)
Quantum aspects of the noncommutative Sine-Gordon model

International Nuclear Information System (INIS)

Kuerkcueoglu

2007-01-01

In this talk, I will first present some of the quantum field theoretical aspects of the integrable noncommutative sine-Gordon model proposed in [hep-th/0406065] using standard semi-classical methods. In particular, I will discuss the fluctuations at quadratic order around the static kink solution using the background field method. I will argue that at 0(θ 2 ) the spectrum of fluctuations remains essentially the same as that of the corresponding commutative theory. A brief analysis of one-loop two-point functions will also be presented and it will be followed by some remarks on the obstacles in determining the noncommutativity corrections to the quantum mass of the kink. (author)
The shear viscosity of the non-commutative plasma

International Nuclear Information System (INIS)

Landsteiner, Karl; Mas, Javier

2007-01-01

We compute the shear viscosity of the non-commutative N = 4 super Yang-Mills quantum field theory at strong coupling using the dual supergravity background. Special interest derives from the fact that the background presents an intrinsic anisotropy in space through the distinction of commutative and non-commutative directions. Despite this anisotropy the analysis exhibits the ubiquitous result η/s = 1/4π for two different shear channels. In order to derive this result, we show that the boundary energy momentum tensor must couple to the open string metric. As a byproduct we compute the renormalised holographic energy momentum tensor and show that it coincides with one in the commutative theory
Non-commutative multiple-valued logic algebras

CERN Document Server

Ciungu, Lavinia Corina

2014-01-01

This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras; a subject which has attracted much interest in the past few years because of its impact on information science, artificial intelligence and other subjects. A study of the newest results in the field, the monograph includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, pseudo-MTL algebras, pseudo-BL algebras and pseudo-MV algebras. It provides a fresh perspective on new trends in logic and algebras in that algebraic structures can be developed into fuzzy logics which connect quantum mechanics, mathematical logic, probability theory, algebra and soft computing. Written in a clear, concise and direct manner, Non-Commutative Multiple-Valued Logic Algebras will be of interest to masters and PhD students, as well as researchers in mathematical logic and theoretical computer science.
LAPLACE-RUNGE-LENZ VECTOR IN QUANTUM MECHANICS IN NONCOMMUTATIVE SPACE

Directory of Open Access Journals (Sweden)

Peter Prešnajder

2014-04-01

Full Text Available The object under scrutiny is the dynamical symmetry connected with conservation of the Laplace-Runge-Lenz vector (LRL in the hydrogen atom problem solved by means of noncommutative quantum mechanics (NCQM. The considered noncommutative configuration space has such a “fuzzy”structure that the rotational invariance is not spoilt. An analogy with the LRL vector in the NCQM is brought to provide our results and also a comparison with the standard QM predictions.
Non-commutative arithmetic circuits with division

Czech Academy of Sciences Publication Activity Database

Hrubeš, Pavel; Wigderson, A.

2015-01-01

Roč. 11, Article 14 (2015), s. 357-393 ISSN 1557-2862 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : arithmetic circuits * non-commutative rational function * skew field Subject RIV: BA - General Mathematics http://theoryofcomputing.org/articles/v011a014/
A contribution of gravity and seismic data in understanding the geometry of the Zouaraa - Ouchtata dune (NW Tunisia): Hydrogeological implications

Science.gov (United States)

Djebbi, M.; Gabtni, H.

2018-01-01

As it is located in a very particular and complex domain within the Tellian fold and thrust belt zone in northwestern Tunisia, the Nefza area has always been challenging. Geological, hydrogeological and geophysical studies were conducted in the region. A multidisciplinary study was performed by combining geological and geophysical techniques. Gravity data processing revealed the continuity of the outcropping series of Argoub Er Romane and Jebel Hamra underneath the dune deposits building a high zone separating the dune of Zouaraa and Ouchtata into two asymmetric basins. It forms a threshold zone that controls the geometry of the dune reservoir in the area. The distribution of the gravity anomaly along the dune of Zouaraa proved the heterogeneity of this dune reservoir. Gravity data modeling for this area confirmed these results and showed a preferential tendency of subsidence to the northwest and thus the thickening of Zouaraa dune sequence as compared to that of Ouchtata.
Noncommutativity from spectral flow

Energy Technology Data Exchange (ETDEWEB)

Heinzl, Thomas; Ilderton, Anton [School of Mathematics and Statistics, University of Plymouth, Drake Circus, Plymouth PL4 8AA (United Kingdom)

2007-07-27

We investigate the transition from second- to first-order systems. Quantum mechanically, this transforms configuration space into phase space and hence introduces noncommutativity in the former. This transition may be described in terms of spectral flow. Gaps in the energy or mass spectrum may become large which effectively truncates the available state space. Using both operator and path integral languages we explicitly discuss examples in quantum mechanics (light-front) quantum field theory and string theory.
Novel ambiguities in the Seiberg-Witten map and the emergent gravity

International Nuclear Information System (INIS)

Muthukumar, B.

2015-01-01

A homogeneous part of the Seiberg-Witten gauge equivalence relation for gauge fields can lead to solutions that involve matter fields in such a way that the gauge equivalence and the dimensional and index structures are preserved. In particular, we consider scalar fields coupled to U(1) gauge fields. The matter fields appear non-linearly in the map. As an application, we analyze the implication of this ambiguity to emergent gravity at the first order in noncommutative parameter and show that the new ambiguity restores the possibility of conformal coupling of real scalar density field that is coupled non-minimally to the emergent gravity induced by gauge fields — a possibility that is strictly not allowed if we consider only the already known ambiguity in the Seiberg-Witten map.

Hydrogeological framework and geometry modeling via joint gravity and borehole parameters, the Nadhour-Sisseb-El Alem basin (central-eastern Tunisia)

Science.gov (United States)

Souei, Ali; Atawa, Mohamed; Zouaghi, Taher

2018-03-01

The Nadhour-Sisseb-El Alem basin, in the central-eastern part of Tunisia, is characterized by the scarcity of surface and subsurface water resources. Although the aquifer systems of this basin are not well understood, the scarce water resources are subject to a high rate of exploitation leading to a significant drop in the level of the water table. This work presents correlation of gravity data with hydrogeological data in order to improve the knowledge of the deep structures and aquifer systems. Various geophysical filtering techniques (e.g., residual anomaly, upward continuation, horizontal gradient, and Euler deconvolution) applied to the complete Bouguer anomaly, deduce the deep structures and geometry of the basin and highlight gravity lineaments that correspond to the tectonic features. The structural framework of the Nadhour-Sisseb-El Alem hydrogeological basin shows N-S to NNE-SSW and E-W oriented structures that should be related to tectonic deformations. In addition to the faults, previously recognized, new lineaments are highlighted by the present work. They correspond to NE-, NW-, E- and N- trending faults that have controlled structuring and geometry of the basin. 2D gravity forward modeling, based on the interpretation of geophysical, geological and hydrogeological data, led to a better understanding of the basin geometry and spatial distribution of the Campanian-Maastrichtian and Cenozoic potential aquifers. Three hydrogeological sub-basins identified include the Nadhour sub-basin in the north, the El Alem sub-Basin in the South and the Etrabelsia sub-Basin in the East. These sub-basins are marked by a thickening of deposits, are separated by the Sisseb-Fadeloun raised structure of Neogene and Quaternary thinned series. The results allow the determination of limit conditions for the basin hydrodynamic evolution and explain some anomalies on the quantity and quality of the groundwater. They provide a management guide for water resources prospection in
Loop calculations for the non-commutative U*(1) gauge field model with oscillator term

International Nuclear Information System (INIS)

Blaschke, Daniel N.; Grosse, Harald; Kronberger, Erwin; Schweda, Manfred; Wohlgenannt, Michael

2010-01-01

Motivated by the success of the non-commutative scalar Grosse-Wulkenhaar model, a non-commutative U * (1) gauge field theory including an oscillator-like term in the action has been put forward in (Blaschke et al. in Europhys. Lett. 79:61002, 2007). The aim of the current work is to analyze whether that action can lead to a fully renormalizable gauge model on non-commutative Euclidean space. In a first step, explicit one-loop graph computations are hence presented, and their results as well as necessary modifications of the action are successively discussed. (orig.)
Chiral gravity, log gravity, and extremal CFT

International Nuclear Information System (INIS)

Maloney, Alexander; Song Wei; Strominger, Andrew

2010-01-01

We show that the linearization of all exact solutions of classical chiral gravity around the AdS 3 vacuum have positive energy. Nonchiral and negative-energy solutions of the linearized equations are infrared divergent at second order, and so are removed from the spectrum. In other words, chirality is confined and the equations of motion have linearization instabilities. We prove that the only stationary, axially symmetric solutions of chiral gravity are BTZ black holes, which have positive energy. It is further shown that classical log gravity--the theory with logarithmically relaxed boundary conditions--has finite asymptotic symmetry generators but is not chiral and hence may be dual at the quantum level to a logarithmic conformal field theories (CFT). Moreover we show that log gravity contains chiral gravity within it as a decoupled charge superselection sector. We formally evaluate the Euclidean sum over geometries of chiral gravity and show that it gives precisely the holomorphic extremal CFT partition function. The modular invariance and integrality of the expansion coefficients of this partition function are consistent with the existence of an exact quantum theory of chiral gravity. We argue that the problem of quantizing chiral gravity is the holographic dual of the problem of constructing an extremal CFT, while quantizing log gravity is dual to the problem of constructing a logarithmic extremal CFT.
A new non-commutative representation of the Wiener and Poisson processes

International Nuclear Information System (INIS)

Privault, N.

1996-01-01

Using two different constructions of the chaotic and variational calculus on Poisson space, we show that the Wiener and Poisson processes have a non-commutative representation which is different from the one obtained by transfer of the Fock space creation and annihilation operators. We obtain in this way an extension of the non-commutative It calculus. The associated commutation relations show a link between the geometric and exponential distributions. (author). 11 refs
On the Chern-Gauss-Bonnet theorem for the noncommutative 4-sphere

Science.gov (United States)

Arnlind, Joakim; Wilson, Mitsuru

2017-01-01

We construct a differential calculus over the noncommutative 4-sphere in the framework of pseudo-Riemannian calculi, and show that for every metric in a conformal class of perturbations of the round metric, there exists a unique metric and torsion-free connection. Furthermore, we find a localization of the projective module corresponding to the space of vector fields, which allows us to formulate a Chern-Gauss-Bonnet type theorem for the noncommutative 4-sphere.
Geometric scalar theory of gravity beyond spherical symmetry

Science.gov (United States)

Moschella, U.; Novello, M.

2017-04-01

We construct several exact solutions for a recently proposed geometric scalar theory of gravity. We focus on a class of axisymmetric geometries and a big-bang-like geometry and discuss their Lorentzian character. The axisymmetric solutions are parametrized by an integer angular momentum l . The l =0 (spherical) case gives rise to the Schwarzschild geometry. The other solutions have naked singular surfaces. While not a priori obvious, all the solutions that we present here are globally Lorentzian. The Lorentzian signature appears to be a robust property of the disformal geometries solving the vacuum geometric scalar theory of gravity equations.
Quantum gravity with matter and group field theory

International Nuclear Information System (INIS)

Krasnov, Kirill

2007-01-01

A generalization of the matrix model idea to quantum gravity in three and higher dimensions is known as group field theory (GFT). In this paper we study generalized GFT models that can be used to describe 3D quantum gravity coupled to point particles. The generalization considered is that of replacing the group leading to pure quantum gravity by the twisted product of the group with its dual-the so-called Drinfeld double of the group. The Drinfeld double is a quantum group in that it is an algebra that is both non-commutative and non-cocommutative, and special care is needed to define group field theory for it. We show how this is done, and study the resulting GFT models. Of special interest is a new topological model that is the 'Ponzano-Regge' model for the Drinfeld double. However, as we show, this model does not describe point particles. Motivated by the GFT considerations, we consider a more general class of models that are defined not using GFT, but the so-called chain mail techniques. A general model of this class does not produce 3-manifold invariants, but has an interpretation in terms of point particle Feynman diagrams
Scalar-graviton interaction in the noncommutative space

International Nuclear Information System (INIS)

Brandt, F. T.; Elias-Filho, M. R.

2006-01-01

We obtain the leading order interaction between the graviton and the neutral scalar boson in the context of noncommutative field theory. Our approach makes use of the Ward identity associated with the invariance under a subgroup of symplectic diffeomorphisms
Noncommutative vector bundles over fuzzy CPN and their covariant derivatives

International Nuclear Information System (INIS)

Dolan, Brian P.; Huet, Idrish; Murray, Sean; O'Connor, Denjoe

2007-01-01

We generalise the construction of fuzzy CP N in a manner that allows us to access all noncommutative equivariant complex vector bundles over this space. We give a simplified construction of polarization tensors on S 2 that generalizes to complex projective space, identify Laplacians and natural noncommutative covariant derivative operators that map between the modules that describe noncommuative sections. In the process we find a natural generalization of the Schwinger-Jordan construction to su(n) and identify composite oscillators that obey a Heisenberg algebra on an appropriate Fock space
On the development of non-commutative translation-invariant quantum gauge field models

International Nuclear Information System (INIS)

Sedmik, R.I.P.

2009-01-01

Aiming to understand the most fundamental principles of nature one has to approach the highest possible energy scales corresponding to the smallest possible distances - the Planck scale. Historically, three different theoretical fields have been developed to treat the problems appearing in this endeavor: string theory, quantum gravity, and non-commutative (NC) quantum field theory (QFT). The latter was originally motivated by the conjecture that the introduction of uncertainty relations between space-time coordinates introduces a natural energy cutoff, which should render the resulting computations well defined and finite. Despite failing to fulfill this expectation, NC physics is a challenging field of research, which has proved to be a fruitful source for new ideas and methods. Mathematically, non-commutativity is implemented by the so called Weyl quantization, giving rise to a modified product - the Groenewold-Moyal product. It realizes an operator ordering, and allows to work within the well established framework of QFT on non-commutative spaces. The main obstacle of NCQFT is the appearance of singularities being shifted from high to low energies. This effect, being referred to as 'uV/IR mixing', is a direct consequence of the deformation of the product, and inhibits or complicates the direct application of well approved renormalization schemes. In order to remedy this problem, several approaches have been worked out during the past decade which, unfortunately, all have shortcomings such as the breaking of translation invariance or an inappropriate alternation of degrees of freedom. Thence, the resulting theories are either being rendered 'unphysical', or considered a priori to be toy models. Nonetheless, these efforts have helped to analyze the mechanisms leading to uV/IR mixing and finally led to the insight that renormalizability can only be achieved by respecting the inherent connection of long and short distances (scales) of NCQFT in the construction of
Quantum Riemannian geometry of phase space and nonassociativity

Directory of Open Access Journals (Sweden)

Beggs Edwin J.

2017-04-01

Full Text Available Noncommutative or ‘quantum’ differential geometry has emerged in recent years as a process for quantizing not only a classical space into a noncommutative algebra (as familiar in quantum mechanics but also differential forms, bundles and Riemannian structures at this level. The data for the algebra quantisation is a classical Poisson bracket while the data for quantum differential forms is a Poisson-compatible connection. We give an introduction to our recent result whereby further classical data such as classical bundles, metrics etc. all become quantised in a canonical ‘functorial’ way at least to 1st order in deformation theory. The theory imposes compatibility conditions between the classical Riemannian and Poisson structures as well as new physics such as typical nonassociativity of the differential structure at 2nd order. We develop in detail the case of ℂℙn where the commutation relations have the canonical form [wi, w̄j] = iλδij similar to the proposal of Penrose for quantum twistor space. Our work provides a canonical but ultimately nonassociative differential calculus on this algebra and quantises the metric and Levi-Civita connection at lowest order in λ.
String states, loops and effective actions in noncommutative field theory and matrix models

Directory of Open Access Journals (Sweden)

Harold C. Steinacker

2016-09-01

Full Text Available Refining previous work by Iso, Kawai and Kitazawa, we discuss bi-local string states as a tool for loop computations in noncommutative field theory and matrix models. Defined in terms of coherent states, they exhibit the stringy features of noncommutative field theory. This leads to a closed form for the 1-loop effective action in position space, capturing the long-range non-local UV/IR mixing for scalar fields. The formalism applies to generic fuzzy spaces. The non-locality is tamed in the maximally supersymmetric IKKT or IIB model, where it gives rise to supergravity. The linearized supergravity interactions are obtained directly in position space at one loop using string states on generic noncommutative branes.
String states, loops and effective actions in noncommutative field theory and matrix models

Energy Technology Data Exchange (ETDEWEB)

Steinacker, Harold C., E-mail: harold.steinacker@univie.ac.at

2016-09-15

Refining previous work by Iso, Kawai and Kitazawa, we discuss bi-local string states as a tool for loop computations in noncommutative field theory and matrix models. Defined in terms of coherent states, they exhibit the stringy features of noncommutative field theory. This leads to a closed form for the 1-loop effective action in position space, capturing the long-range non-local UV/IR mixing for scalar fields. The formalism applies to generic fuzzy spaces. The non-locality is tamed in the maximally supersymmetric IKKT or IIB model, where it gives rise to supergravity. The linearized supergravity interactions are obtained directly in position space at one loop using string states on generic noncommutative branes.
Higgs production in e−e+ collisions as a probe of noncommutativity

International Nuclear Information System (INIS)

Ghasemkhani, M.; Goldouzian, R.; Khanpour, H.; Yanehsari, M. Khatiri; Najafabadi, M. Mohammadi

2014-01-01

We examine the sensitivity of the angular distribution of the Higgs boson in the process of e + e − →ZH and the total cross section in the minimal noncommutative standard model (mNCSM) framework to set a lower limit on the noncommutative characteristic scale (Λ). In contrast to the standard model case, in this process the Higgs boson tends to be emitted anisotropically in the transverse plane. Based on this fact, the profile likelihood ratio is used to set the lower limit on Λ. The lower limit is presented as a function of the integrated luminosity. We show that at a center-of-mass energy of 1.5 TeV and with 500 fb −1 of data, the noncommutative characteristic energy scale Λ can be excluded up to 1.2 TeV
Non-Commutative Integration, Zeta Functions and the Haar State for SUq(2)

International Nuclear Information System (INIS)

Matassa, Marco

2015-01-01

We study a notion of non-commutative integration, in the spirit of modular spectral triples, for the quantum group SU q (2). In particular we define the non-commutative integral as the residue at the spectral dimension of a zeta function, which is constructed using a Dirac operator and a weight. We consider the Dirac operator introduced by Kaad and Senior and a family of weights depending on two parameters, which are related to the diagonal automorphisms of SU q (2). We show that, after fixing one of the parameters, the non-commutative integral coincides with the Haar state of SU q (2). Moreover we can impose an additional condition on the zeta function, which also fixes the second parameter. For this unique choice the spectral dimension coincides with the classical dimension
Poisson geometry from a Dirac perspective

Science.gov (United States)

Meinrenken, Eckhard

2018-03-01

We present proofs of classical results in Poisson geometry using techniques from Dirac geometry. This article is based on mini-courses at the Poisson summer school in Geneva, June 2016, and at the workshop Quantum Groups and Gravity at the University of Waterloo, April 2016.
Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model

International Nuclear Information System (INIS)

Chamseddine, Ali H.; Connes, Alain

2007-01-01

The purpose of this Letter is to remove the arbitrariness of the ad hoc choice of the algebra and its representation in the noncommutative approach to the standard model, which was begging for a conceptual explanation. We assume as before that space-time is the product of a four-dimensional manifold by a finite noncommmutative space F. The spectral action is the pure gravitational action for the product space. To remove the above arbitrariness, we classify the irreducible geometries F consistent with imposing reality and chiral conditions on spinors, to avoid the fermion doubling problem, which amounts to have total dimension 10 (in the K-theoretic sense). It gives, almost uniquely, the standard model with all its details, predicting the number of fermions per generation to be 16, their representations and the Higgs breaking mechanism, with very little input
Search of wormholes in different dimensional non-commutative inspired space-times with Lorentzian distribution

Energy Technology Data Exchange (ETDEWEB)

Bhar, Piyali; Rahaman, Farook [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India)

2014-12-01

In this paper we ask whether the wormhole solutions exist in different dimensional noncommutativity-inspired spacetimes. It is well known that the noncommutativity of the space is an outcome of string theory and it replaced the usual point-like object by a smeared object. Here we have chosen the Lorentzian distribution as the density function in the noncommutativity-inspired spacetime. We have observed that the wormhole solutions exist only in four and five dimensions; however, in higher than five dimensions no wormhole exists. For five dimensional spacetime, we get a wormhole for a restricted region. In the usual four dimensional spacetime, we get a stable wormhole which is asymptotically flat. (orig.)
gravity

Indian Academy of Sciences (India)

We study the cosmological dynamics for R p exp( λ R ) gravity theory in the metric formalism, using dynamical systems approach. Considering higher-dimensional FRW geometries in case of an imperfect fluid which has two different scale factors in the normal and extra dimensions, we find the exact solutions, and study its ...
Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces

Science.gov (United States)

Meljanac, Stjepan; Krešić–Jurić, Saša; Martinić, Tea

2017-07-01

This paper investigates bicovariant differential calculus on noncommutative spaces of the Lie algebra type. For a given Lie algebra g0, we construct a Lie superalgebra g =g0⊕g1 containing noncommutative coordinates and one-forms. We show that g can be extended by a set of generators TAB whose action on the enveloping algebra U (g ) gives the commutation relations between monomials in U (g0 ) and one-forms. Realizations of noncommutative coordinates, one-forms, and the generators TAB as formal power series in a semicompleted Weyl superalgebra are found. In the special case dim(g0 ) =dim(g1 ) , we also find a realization of the exterior derivative on U (g0 ) . The realizations of these geometric objects yield a bicovariant differential calculus on U (g0 ) as a deformation of the standard calculus on the Euclidean space.

Quantum theories on noncommutative spaces with nontrivial topology: Aharonov-Bohm and Casimir effects

International Nuclear Information System (INIS)

Chaichian, M.; Tureanu, A.; Demichev, A.; Presnajder, P.; Sheikh-Jabbari, M.M.

2001-02-01

After discussing the peculiarities of quantum systems on noncommutative (NC) spaces with nontrivial topology and the operator representation of the *-product on them, we consider the Aharonov-Bohm and Casimir effects for such spaces. For the case of the Aharonov-Bohm effect, we have obtained an explicit expression for the shift of the phase, which is gauge invariant in the NC sense. The Casimir energy of a field theory on a NC cylinder is divergent, while it becomes finite on a torus, when the dimensionless parameter of noncommutativity is a rational number. The latter corresponds to a well-defined physical picture. Certain distinctions from other treatments based on a different way of taking the noncommutativity into account are also discussed. (author)
Vaidya spacetime in massive gravity's rainbow

Directory of Open Access Journals (Sweden)

Yaghoub Heydarzade

2017-11-01

Full Text Available In this paper, we will analyze the energy dependent deformation of massive gravity using the formalism of massive gravity's rainbow. So, we will use the Vainshtein mechanism and the dRGT mechanism for the energy dependent massive gravity, and thus analyze a ghost free theory of massive gravity's rainbow. We study the energy dependence of a time-dependent geometry, by analyzing the radiating Vaidya solution in this theory of massive gravity's rainbow. The energy dependent deformation of this Vaidya metric will be performed using suitable rainbow functions.
Noncommutative phase spaces on Aristotle group

Directory of Open Access Journals (Sweden)

Ancille Ngendakumana

2012-03-01

Full Text Available We realize noncommutative phase spaces as coadjoint orbits of extensions of the Aristotle group in a two dimensional space. Through these constructions the momenta of the phase spaces do not commute due to the presence of a naturally introduced magnetic eld. These cases correspond to the minimal coupling of the momentum with a magnetic potential.
On total noncommutativity in quantum mechanics

Science.gov (United States)

Lahti, Pekka J.; Ylinen, Kari

1987-11-01

It is shown within the Hilbert space formulation of quantum mechanics that the total noncommutativity of any two physical quantities is necessary for their satisfying the uncertainty relation or for their being complementary. The importance of these results is illustrated with the canonically conjugate position and momentum of a free particle and of a particle closed in a box.
Noncommutative Yang-Mills from equivalence of star products

International Nuclear Information System (INIS)

Jurco, B.; Schupp, P.

2000-01-01

It is shown that the transformation between ordinary and noncommutative Yang-Mills theory as formulated by Seiberg and Witten is due to the equivalence of certain star products on the D-brane world-volume. (orig.)
Noncommutative Yang-Mills from equivalence of star products

Energy Technology Data Exchange (ETDEWEB)

Jurco, B. [Max-Planck-Institut fuer Mathematik, Bonn (Germany); Schupp, P. [Sektion Physik, Universitaet Muenchen, Theresienstrasse 37, 80333 Muenchen (Germany)

2000-05-01

It is shown that the transformation between ordinary and noncommutative Yang-Mills theory as formulated by Seiberg and Witten is due to the equivalence of certain star products on the D-brane world-volume. (orig.)
Noncommutative quantum mechanics

Science.gov (United States)

Gamboa, J.; Loewe, M.; Rojas, J. C.

2001-09-01

A general noncommutative quantum mechanical system in a central potential V=V(r) in two dimensions is considered. The spectrum is bounded from below and, for large values of the anticommutative parameter θ, we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction V(r) is replaced by V=V(HHO,Lz), where HHO is the Hamiltonian of the two-dimensional harmonic oscillator and Lz is the z component of the angular momentum. For other finite values of θ the model can be solved by using perturbation theory.
WWNPQFT-2011 - Abstracts

International Nuclear Information System (INIS)

Bianchi, E.; Bender, C.; Culetu, H.; Fried, H.; Grossmann, A.; Hofmann, R.; Le Bellac, M.; Martinetti, P.; Muller, B.; Patras, F.; Raffaeli, B.; Vitting Andersen, J.

2013-01-01

The object of this workshop is to consolidate and publicize new efforts in non-perturbative field theories. This year the presentations deal with quantum gravity, non-commutative geometry, fat-tailed wave-functions, strongly coupled field theories, space-times two time-like dimensions, and multiplicative renormalization. A presentation is dedicated to the construction of a nucleon-nucleon potential from an analytical, non-perturbative gauge invariant QCD. This document gathers the abstracts of the presentations
The geometric role of symmetry breaking in gravity

International Nuclear Information System (INIS)

Wise, Derek K

2012-01-01

In gravity, breaking symmetry from a group G to a group H plays the role of describing geometry in relation to the geometry of the homogeneous space G/H. The deep reason for this is Cartan's 'method of equivalence,' giving, in particular, an exact correspondence between metrics and Cartan connections. I argue that broken symmetry is thus implicit in any gravity theory, for purely geometric reasons. As an application, I explain how this kind of thinking gives a new approach to Hamiltonian gravity in which an observer field spontaneously breaks Lorentz symmetry and gives a Cartan connection on space.
Simplicial quantum gravity

International Nuclear Information System (INIS)

Hartle, J.B.

1985-01-01

Simplicial approximation and the ideas associated with the Regge calculus provide a concrete way of implementing a sum over histories formulation of quantum gravity. A simplicial geometry is made up of flat simplices joined together in a prescribed way together with an assignment of lengths to their edges. A sum over simplicial geometries is a sum over the different ways the simplices can be joined together with an integral over their edge lengths. The construction of the simplicial Euclidean action for this approach to quantum general relativity is illustrated. The recovery of the diffeomorphism group in the continuum limit is discussed. Some possible classes of simplicial complexes with which to define a sum over topologies are described. In two dimensional quantum gravity it is argued that a reasonable class is the class of pseudomanifolds
Newton-Cartan gravity and torsion

Science.gov (United States)

Bergshoeff, Eric; Chatzistavrakidis, Athanasios; Romano, Luca; Rosseel, Jan

2017-10-01

We compare the gauging of the Bargmann algebra, for the case of arbitrary torsion, with the result that one obtains from a null-reduction of General Relativity. Whereas the two procedures lead to the same result for Newton-Cartan geometry with arbitrary torsion, the null-reduction of the Einstein equations necessarily leads to Newton-Cartan gravity with zero torsion. We show, for three space-time dimensions, how Newton-Cartan gravity with arbitrary torsion can be obtained by starting from a Schrödinger field theory with dynamical exponent z = 2 for a complex compensating scalar and next coupling this field theory to a z = 2 Schrödinger geometry with arbitrary torsion. The latter theory can be obtained from either a gauging of the Schrödinger algebra, for arbitrary torsion, or from a null-reduction of conformal gravity.
Moving vortices in noncommutative gauge theory

International Nuclear Information System (INIS)

Horvathy, P.A.; Stichel, P.C.

2004-01-01

Exact time-dependent solutions of nonrelativistic noncommutative Chern-Simons gauge theory are presented in closed analytic form. They are different from (indeed orthogonal to) those discussed recently by Hadasz, Lindstroem, Rocek and von Unge. Unlike theirs, our solutions can move with an arbitrary constant velocity, and can be obtained from the previously known static solutions by the recently found 'exotic' boost symmetry
Noncommutative differential forms on the kappa-deformed space

International Nuclear Information System (INIS)

Meljanac, Stjepan; Kresic-Juric, Sasa

2009-01-01

We construct a differential algebra of forms on the kappa-deformed space. For a given realization of noncommutative coordinates as formal power series in the Weyl algebra we find an infinite family of one-forms and nilpotent exterior derivatives. We derive explicit expressions for the exterior derivative and one-forms in covariant and noncovariant realizations. We also introduce higher order forms and show that the exterior derivative satisfies the graded Leibniz rule. The differential forms are generally not graded commutative, but they satisfy the graded Jacobi identity. We also consider the star-product of classical differential forms. The star-product is well defined if the commutator between the noncommutative coordinates and one-forms is closed in the space of one-forms alone. In addition, we show that in certain realizations the exterior derivative acting on the star-product satisfies the undeformed Leibniz rule.
Quadratic algebras and noncommutative integration of Klein-Gordon equations in non-steckel Riemann spaces

International Nuclear Information System (INIS)

Varaksin, O.L.; Firstov, V.V.; Shapovalov, A.V.; Shirokov, I.V.

1995-01-01

The method of noncommutative integration of linear partial differential equations is used to solve the Klein-Gordon equations in Riemann space, in the case when the set of noncommutating symmetry operators of this equation for a quadratic algebra consists of one second-order operator and several first-order operators. Solutions that do not permit variable separation are presented
Infinite volume of noncommutative black hole wrapped by finite surface

Energy Technology Data Exchange (ETDEWEB)

Zhang, Baocheng, E-mail: zhangbc.zhang@yahoo.com [School of Mathematics and Physics, China University of Geosciences, Wuhan 430074 (China); You, Li, E-mail: lyou@mail.tsinghua.edu.cn [State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084 (China)

2017-02-10

The volume of a black hole under noncommutative spacetime background is found to be infinite, in contradiction with the surface area of a black hole, or its Bekenstein–Hawking (BH) entropy, which is well-known to be finite. Our result rules out the possibility of interpreting the entropy of a black hole by counting the number of modes wrapped inside its surface if the final evaporation stage can be properly treated. It implies the statistical interpretation for the BH entropy can be independent of the volume, provided spacetime is noncommutative. The effect of radiation back reaction is found to be small and doesn't influence the above conclusion.
Dolan-Grady relations and noncommutative quasi-exactly solvable systems

International Nuclear Information System (INIS)

Klishevich, Sergey M; Plyushchay, Mikhail S

2003-01-01

We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives obeying the nonlinear Dolan-Grady relations. This restricts the structure function of the deformed oscillator algebra to a quadratic polynomial. The cases when the coordinates form the su(2) and sl(2,R) algebras are investigated in detail. Reducing the Hamiltonian to 1D finite-difference quasi-exactly solvable operators, we demonstrate partial algebraization of the spectrum of the corresponding systems on the fuzzy sphere and noncommutative hyperbolic plane. A completely covariant method based on the notion of intrinsic algebra is proposed to deal with the spectral problem of such systems
Butterfly effect and holographic mutual information under external field and spatial noncommutativity

Energy Technology Data Exchange (ETDEWEB)

Huang, Wung-Hong; Du, Yi-Hsien [Department of Physics, National Cheng Kung University,No. 1, University Road, Tainan City 701, Taiwan (China)

2017-02-07

We apply the transformation of mixing azimuthal and internal coordinate or mixing time and internal coordinate to a stack of N black M-branes to find the Melvin spacetime of a stack of N black D-branes with magnetic or electric flux in string theory, after the Kaluza-Klein reduction. We slightly extend previous formulas to investigate the external magnetic and electric effects on the butterfly effect and holographic mutual information. It shows that the Melvin fields do not modify the scrambling time and will enhance the mutual information. In addition, we also T-dualize and twist a stack of N black D-branes to find a Melvin Universe supported by the flux of the NSNS b-field, which describes a non-comutative spacetime. It also shows that the spatial noncommutativity does not modify the scrambling time and will enhance the mutual information. We also study the corrected mutual information in the backreaction geometry due to the shock wave in our three model spacetimes.
Gravity's rainbow: A bridge between LQC and DSR

Directory of Open Access Journals (Sweden)

M.A. Gorji

2017-02-01

Full Text Available The doubly special relativity (DSR theories are constructed in order to take into account an observer-independent length scale in special relativity framework. Gravity's rainbow is a simple generalization of DSR theories to incorporate gravity. In this paper, we show that the effective Friedmann equations that are suggested by loop quantum cosmology (LQC can be exactly reobtained in rainbow cosmology setup. The deformed geometry of LQC then fixes the modified dispersion relation and results in a unique DSR model. In comparison with standard LQC scenario where only the geometry is modified, both geometry and matter parts get modified in our setup. In this respect, we show that the total number of microstates for the universe is finite which suggests the statistical origin of the energy and entropy density bounds. These results explicitly show that the DSR theories are appropriate candidates for the flat limit of loop quantum gravity.
Chirality Quantum Phase Transition in Noncommutative Dirac Oscillator

International Nuclear Information System (INIS)

Wang Shao-Hua; Hou Yu-Long; Jing Jian; Wang Qing; Long Zheng-Wen

2014-01-01

The charged Dirac oscillator on a noncommutative plane coupling to a uniform perpendicular magnetic held is studied in this paper. We map the noncommutative plane to a commutative one by means of Bopp shift and study this problem on the commutative plane. We find that this model can be mapped onto a quantum optics model which contains Anti—Jaynes—Cummings (AJC) or Jaynes—Cummings (JC) interactions when a dimensionless parameter ζ (which is the function of the intensity of the magnetic held) takes values in different regimes. Furthermore, this model behaves as experiencing a chirality quantum phase transition when the dimensionless parameter ζ approaches the critical point. Several evidences of the chirality quantum phase transition are presented. We also study the non-relativistic limit of this model and find that a similar chirality quantum phase transition takes place in its non-relativistic limit. (physics of elementary particles and fields)
Space/time non-commutative field theories and causality

International Nuclear Information System (INIS)

Bozkaya, H.; Fischer, P.; Pitschmann, M.; Schweda, M.; Grosse, H.; Putz, V.; Wulkenhaar, R.

2003-01-01

As argued previously, amplitudes of quantum field theories on non-commutative space and time cannot be computed using naive path integral Feynman rules. One of the proposals is to use the Gell-Mann-Low formula with time-ordering applied before performing the integrations. We point out that the previously given prescription should rather be regarded as an interaction-point time-ordering. Causality is explicitly violated inside the region of interaction. It is nevertheless a consistent procedure, which seems to be related to the interaction picture of quantum mechanics. In this framework we compute the one-loop self-energy for a space/time non-commutative φ 4 theory. Although in all intermediate steps only three-momenta play a role, the final result is manifestly Lorentz covariant and agrees with the naive calculation. Deriving the Feynman rules for general graphs, we show, however, that such a picture holds for tadpole lines only. (orig.)

Time-dependent transitions with time–space noncommutativity and its implications in quantum optics

International Nuclear Information System (INIS)

Chandra, Nitin

2012-01-01

We study the time-dependent transitions of a quantum-forced harmonic oscillator in noncommutative R 1,1 perturbatively to linear order in the noncommutativity θ. We show that the Poisson distribution gets modified, and that the vacuum state evolves into a ‘squeezed’ state rather than a coherent state. The time evolutions of uncertainties in position and momentum in vacuum are also studied and imply interesting consequences for modeling nonlinear phenomena in quantum optics. (paper)
A novel noncommutative KdV-type equation, its recursion operator, and solitons

Science.gov (United States)

Carillo, Sandra; Lo Schiavo, Mauro; Porten, Egmont; Schiebold, Cornelia

2018-04-01

A noncommutative KdV-type equation is introduced extending the Bäcklund chart in Carillo et al. [Symmetry Integrability Geom.: Methods Appl. 12, 087 (2016)]. This equation, called meta-mKdV here, is linked by Cole-Hopf transformations to the two noncommutative versions of the mKdV equations listed in Olver and Sokolov [Commun. Math. Phys. 193, 245 (1998), Theorem 3.6]. For this meta-mKdV, and its mirror counterpart, recursion operators, hierarchies, and an explicit solution class are derived.
Quantum mechanical systems interacting with different polarizations of gravitational waves in noncommutative phase space

Science.gov (United States)

Saha, Anirban; Gangopadhyay, Sunandan; Saha, Swarup

2018-02-01

Owing to the extreme smallness of any noncommutative scale that may exist in nature, both in the spatial and momentum sector of the quantum phase space, a credible possibility of their detection lies in the gravitational wave (GW) detection scenario, where one effectively probes the relative length-scale variations ˜O [10-20-10-23] . With this motivation, we have theoretically constructed how a free particle and a harmonic oscillator will respond to linearly and circularly polarized gravitational waves if their quantum mechanical phase space has a noncommutative structure. We critically analyze the formal solutions which show resonance behavior in the responses of both free particle and HO systems to GW with both kind of polarizations. We discuss the possible implications of these solutions in detecting noncommutativity in a GW detection experiment. We use the currently available upper-bound estimates on various noncommutative parameters to anticipate the relative importance of various terms in the solutions. We also argue how the quantum harmonic oscillator system we considered here can be very relevant in the context of the resonant bar detectors of GW which are already operational.
On the UV renormalizability of noncommutative field theories

International Nuclear Information System (INIS)

Sarkar, Swarnendu

2002-01-01

UV/IR mixing is one of the most important features of noncommutative field theories. As a consequence of this coupling of the UV and IR sectors, the configuration of fields at the zero momentum limit in these theories is a very singular configuration. We show that the renormalization conditions set at a particular momentum configuration with a fixed number of zero momenta, renormalizes the Green's functions for any general momenta only when this configuration has same set of zero momenta. Therefore only when renormalization conditions are set at a point where all the external momenta are nonzero, the quantum theory is renormalizable for all values of nonzero momentum. This arises as a result of different scaling behaviors of Green's functions with respect to the UV cutoff (Λ) for configurations containing different set of zero momenta. We study this in the noncommutative φ 4 theory and analyse similar results for the Gross-Neveu model at one loop level. We next show this general feature using Wilsonian RG of Polchinski in the globally O(N) symmetric scalar theory and prove the renormalizability of the theory to all orders with an infrared cutoff. In the context of spontaneous symmetry breaking (SSB) in noncommutative scalar theory, it is essential to note the different scaling behaviors of Green's functions with respect to Λ for different set of zero momenta configurations. We show that in the broken phase of the theory the Ward identities are satisfied to all orders only when one keeps an infrared regulator by shifting to a nonconstant vacuum. (author)
Dolan Grady relations and noncommutative quasi-exactly solvable systems

Science.gov (United States)

Klishevich, Sergey M.; Plyushchay, Mikhail S.

2003-11-01

We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives obeying the nonlinear Dolan-Grady relations. This restricts the structure function of the deformed oscillator algebra to a quadratic polynomial. The cases when the coordinates form the {\\mathfrak{su}}(2) and {\\mathfrak{sl}}(2,{\\bb {R}}) algebras are investigated in detail. Reducing the Hamiltonian to 1D finite-difference quasi-exactly solvable operators, we demonstrate partial algebraization of the spectrum of the corresponding systems on the fuzzy sphere and noncommutative hyperbolic plane. A completely covariant method based on the notion of intrinsic algebra is proposed to deal with the spectral problem of such systems.
An algebraic scheme associated with the non-commutative KP hierarchy and some of its extensions

International Nuclear Information System (INIS)

Dimakis, Aristophanes; Mueller-Hoissen, Folkert

2005-01-01

A well-known ansatz ('trace method') for soliton solutions turns the equations of the (non-commutative) KP hierarchy, and those of certain extensions, into families of algebraic sum identities. We develop an algebraic formalism, in particular involving a (mixable) shuffle product, to explore their structure. More precisely, we show that the equations of the non-commutative KP hierarchy and its extension (xncKP) in the case of a Moyal-deformed product, as derived in previous work, correspond to identities in this algebra. Furthermore, the Moyal product is replaced by a more general associative product. This leads to a new even more general extension of the non-commutative KP hierarchy. Relations with Rota-Baxter algebras are established
Sums over geometries and improvements on the mean field approximation

International Nuclear Information System (INIS)

Sacksteder, Vincent E. IV

2007-01-01

The saddle points of a Lagrangian due to Efetov are analyzed. This Lagrangian was originally proposed as a tool for calculating systematic corrections to the Bethe approximation, a mean-field approximation which is important in statistical mechanics, glasses, coding theory, and combinatorial optimization. Detailed analysis shows that the trivial saddle point generates a sum over geometries reminiscent of dynamically triangulated quantum gravity, which suggests new possibilities to design sums over geometries for the specific purpose of obtaining improved mean-field approximations to D-dimensional theories. In the case of the Efetov theory, the dominant geometries are locally treelike, and the sum over geometries diverges in a way that is similar to quantum gravity's divergence when all topologies are included. Expertise from the field of dynamically triangulated quantum gravity about sums over geometries may be able to remedy these defects and fulfill the Efetov theory's original promise. The other saddle points of the Efetov Lagrangian are also analyzed; the Hessian at these points is nonnormal and pseudo-Hermitian, which is unusual for bosonic theories. The standard formula for Gaussian integrals is generalized to nonnormal kernels
Spectral dimension of quantum geometries

International Nuclear Information System (INIS)

Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes

2014-01-01

The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth geometries but also on discrete (e.g., simplicial) ones. In this paper, we consider the spectral dimension of quantum states of spatial geometry defined on combinatorial complexes endowed with additional algebraic data: the kinematical quantum states of loop quantum gravity (LQG). Preliminarily, the effects of topology and discreteness of classical discrete geometries are studied in a systematic manner. We look for states reproducing the spectral dimension of a classical space in the appropriate regime. We also test the hypothesis that in LQG, as in other approaches, there is a scale dependence of the spectral dimension, which runs from the topological dimension at large scales to a smaller one at short distances. While our results do not give any strong support to this hypothesis, we can however pinpoint when the topological dimension is reproduced by LQG quantum states. Overall, by exploring the interplay of combinatorial, topological and geometrical effects, and by considering various kinds of quantum states such as coherent states and their superpositions, we find that the spectral dimension of discrete quantum geometries is more sensitive to the underlying combinatorial structures than to the details of the additional data associated with them. (paper)
Investigations on the renormalizability of a non-commutative u(1) gauge theory

International Nuclear Information System (INIS)

Rofner, A.

2009-01-01

When considering very small scales near the Planck-length, or equivalently very high energies (far from being reached by today's particle accelerators), space-time is expected to be quantized. Today, all but one forces governing nature (i.e. gravitation) are described via Quantum Field Theories (short QFTs) and more precisely gauge field theories (GFTs). Their heart is the art of renormalization, which allows to handle the divergences for high internal momenta appearing in the course of the perturbative development of the action in a consistent manner. Over the last years numerous attempts have been made to formulate consistent and renormalizable theories also on non-commutative spaces. Yet, it is the latter that represents a major problem for non-commutative QFTs: generally, the non-commutativity is implemented via the so-called star product, which in the simplest case is given by the Moyal-Weyl product, and which leads to a modification of the interaction terms of the theories by introducing additional phase factors depending on the non-commutative parameter theta. Then, this phase leads to a mixing of high and low energies, which is directly linked to the appearance of a new class of divergences for small momenta. While there exist various traditional renormalization schemes in order to handle uV divergences, their counterparts in the IR sector form a major obstacle in formulating consistent non-commutative QFTs. However, a first way out of this misery could be achieved by Grosse and Wulkenhaar for a scalar model. The idea was to add a suitable term to the action, in their case an oscillator term, leading to a decoupling of the high and low energy sectors. Later, the same philosophy has been followed by Gurau et. al. by adding a 1/p 2 like term to the scalar action. Both models have been shown to be renormalizable, and additionally, the latter model leads to a translation invariant propagator, which implies momentum conservation in all space points. Now, the
Non-Commutative Integration, Zeta Functions and the Haar State for SU{sub q}(2)

Energy Technology Data Exchange (ETDEWEB)

Matassa, Marco, E-mail: marco.matassa@gmail.com [SISSA (Italy)

2015-12-15

We study a notion of non-commutative integration, in the spirit of modular spectral triples, for the quantum group SU{sub q}(2). In particular we define the non-commutative integral as the residue at the spectral dimension of a zeta function, which is constructed using a Dirac operator and a weight. We consider the Dirac operator introduced by Kaad and Senior and a family of weights depending on two parameters, which are related to the diagonal automorphisms of SU{sub q}(2). We show that, after fixing one of the parameters, the non-commutative integral coincides with the Haar state of SU{sub q}(2). Moreover we can impose an additional condition on the zeta function, which also fixes the second parameter. For this unique choice the spectral dimension coincides with the classical dimension.
Local field theory on κ-Minkowski space, star products and noncommutative translations

International Nuclear Information System (INIS)

Kosinski, P.; Maslanka, P.; Lukierski, J.

2000-01-01

We consider local field theory on κ-deformed Minkowski space which is an example of solvable Lie-algebraic noncommutative structure. Using integration formula over κ-Minkowski space and κ-deformed Fourier transform, we consider for deformed local fields the reality conditions as well as deformation of action functionals in standard Minkowski space. We present explicit formulas for two equivalent star products describing CBH quantization of field theory on κ-Minkowski space. We express also via star product technique the noncommutative translations in κ-Minkowski space by commutative translations in standard Minkowski space. (author)
CDT meets Horava-Lifshitz gravity

International Nuclear Information System (INIS)

Ambjorn, J.; Goerlich, A.; Jordan, S.; Jurkiewicz, J.; Loll, R.

2010-01-01

The theory of causal dynamical triangulations (CDT) attempts to define a nonperturbative theory of quantum gravity as a sum over spacetime geometries. One of the ingredients of the CDT framework is a global time foliation, which also plays a central role in the quantum gravity theory recently formulated by Horava. We show that the phase diagram of CDT bears a striking resemblance with the generic Lifshitz phase diagram appealed to by Horava. We argue that CDT might provide a unifying nonperturbative framework for anisotropic as well as isotropic theories of quantum gravity.
Simulating Gravity

Science.gov (United States)

Pipinos, Savas

2010-01-01

This article describes one classroom activity in which the author simulates the Newtonian gravity, and employs the Euclidean Geometry with the use of new technologies (NT). The prerequisites for this activity were some knowledge of the formulae for a particle free fall in Physics and most certainly, a good understanding of the notion of similarity…
Noncommutativity and Duality through the Symplectic Embedding Formalism

Directory of Open Access Journals (Sweden)

Everton M.C. Abreu

2010-07-01

Full Text Available This work is devoted to review the gauge embedding of either commutative and noncommutative (NC theories using the symplectic formalism framework. To sum up the main features of the method, during the process of embedding, the infinitesimal gauge generators of the gauge embedded theory are easily and directly chosen. Among other advantages, this enables a greater control over the final Lagrangian and brings some light on the so-called ''arbitrariness problem''. This alternative embedding formalism also presents a way to obtain a set of dynamically dual equivalent embedded Lagrangian densities which is obtained after a finite number of steps in the iterative symplectic process, oppositely to the result proposed using the BFFT formalism. On the other hand, we will see precisely that the symplectic embedding formalism can be seen as an alternative and an efficient procedure to the standard introduction of the Moyal product in order to produce in a natural way a NC theory. In order to construct a pedagogical explanation of the method to the nonspecialist we exemplify the formalism showing that the massive NC U(1 theory is embedded in a gauge theory using this alternative systematic path based on the symplectic framework. Further, as other applications of the method, we describe exactly how to obtain a Lagrangian description for the NC version of some systems reproducing well known theories. Naming some of them, we use the procedure in the Proca model, the irrotational fluid model and the noncommutative self-dual model in order to obtain dual equivalent actions for these theories. To illustrate the process of noncommutativity introduction we use the chiral oscillator and the nondegenerate mechanics.
McVittie solution in f(T) gravity

Energy Technology Data Exchange (ETDEWEB)

Bejarano, Cecilia; Jose Guzman, Maria [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Ferraro, Rafael [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Universidad de Buenos Aires, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina)

2017-12-15

We show that McVittie geometry, which describes a black hole embedded in a FLRW universe, not only solves the Einstein equations but also remains as a non-deformable solution of f(T) gravity. This search for GR solutions that survive in f(T) gravity is facilitated by a null tetrad approach. We also show that flat FLRW geometry is a consistent solution of f(T) dynamical equations not only for T = -6H{sup 2} but also for T = 0, which could be a manifestation of the additional degrees of freedom involved in f(T) theories. (orig.)
McVittie solution in f(T) gravity

International Nuclear Information System (INIS)

Bejarano, Cecilia; Jose Guzman, Maria; Ferraro, Rafael

2017-01-01

We show that McVittie geometry, which describes a black hole embedded in a FLRW universe, not only solves the Einstein equations but also remains as a non-deformable solution of f(T) gravity. This search for GR solutions that survive in f(T) gravity is facilitated by a null tetrad approach. We also show that flat FLRW geometry is a consistent solution of f(T) dynamical equations not only for T = -6H 2 but also for T = 0, which could be a manifestation of the additional degrees of freedom involved in f(T) theories. (orig.)
Non-isospectral flows of noncommutative differential-difference KP equation

International Nuclear Information System (INIS)

Huang, Lin; Ilangovane, R.; Tamizhmani, K.M.; Zhang, Da-jun

2013-01-01

We present master symmetries of noncommutative differential-difference KP equation by considering Sato approach, where the field variables are defined over associative algebras. The Lie algebraic structures of generalized and master symmetries are given. They form a Virasoro Lie algebraic structure
Emergent gravity on covariant quantum spaces in the IKKT model

Energy Technology Data Exchange (ETDEWEB)

Steinacker, Harold C. [Faculty of Physics, University of Vienna,Boltzmanngasse 5, A-1090 Vienna (Austria)

2016-12-30

We study perturbations of 4-dimensional fuzzy spheres as backgrounds in the IKKT or IIB matrix model. Gauge fields and metric fluctuations are identified among the excitation modes with lowest spin, supplemented by a tower of higher-spin fields. They arise from an internal structure which can be viewed as a twisted bundle over S{sup 4}, leading to a covariant noncommutative geometry. The linearized 4-dimensional Einstein equations are obtained from the classical matrix model action under certain conditions, modified by an IR cutoff. Some one-loop contributions to the effective action are computed using the formalism of string states.
Ultradiscrete sine-Gordon Equation over Symmetrized Max-Plus Algebra, and Noncommutative Discrete and Ultradiscrete sine-Gordon Equations

Directory of Open Access Journals (Sweden)

Kenichi Kondo

2013-11-01

Full Text Available Ultradiscretization with negative values is a long-standing problem and several attempts have been made to solve it. Among others, we focus on the symmetrized max-plus algebra, with which we ultradiscretize the discrete sine-Gordon equation. Another ultradiscretization of the discrete sine-Gordon equation has already been proposed by previous studies, but the equation and the solutions obtained here are considered to directly correspond to the discrete counterpart. We also propose a noncommutative discrete analogue of the sine-Gordon equation, reveal its relations to other integrable systems including the noncommutative discrete KP equation, and construct multisoliton solutions by a repeated application of Darboux transformations. Moreover, we derive a noncommutative ultradiscrete analogue of the sine-Gordon equation and its 1-soliton and 2-soliton solutions, using the symmetrized max-plus algebra. As a result, we have a complete set of commutative and noncommutative versions of continuous, discrete, and ultradiscrete sine-Gordon equations.
A quantum Goldman bracket in (2 + 1) quantum gravity

International Nuclear Information System (INIS)

Nelson, J E; Picken, R F

2008-01-01

In the context of quantum gravity for spacetimes of dimension (2 + 1), we describe progress in the construction of a quantum Goldman bracket for intersecting loops on surfaces. Using piecewise linear paths in R 2 (representing loops on the spatial manifold, i.e. the torus) and a quantum connection with noncommuting components, we review how holonomies and Wilson loops for two homotopic paths are related by phases in terms of the signed area between them. Paths rerouted at intersection points with other paths occur on the rhs of the Goldman bracket. To better understand their nature we introduce the concept of integer points inside the parallelogram spanned by two intersecting paths, and show that the rerouted paths must necessarily pass through these integer points

Determinants of self-employment among commuters and non-commuters

DEFF Research Database (Denmark)

Backman, M.; Karlsson, C.

2016-01-01

We analyse the determinants of self-employment and focus on the contextual environment. By distinguishing between commuters and non-commuters we are able to analyse the influence from the work and home environment, respectively. Our results indicate a significant difference between non...
Zeta functions for the spectrum of the non-commutative harmonic oscillators

CERN Document Server

Ichinose, T

2004-01-01

This paper investigates the spectral zeta function of the non-commutative harmonic oscillator studied in \\cite{PW1, 2}. It is shown, as one of the basic analytic properties, that the spectral zeta function is extended to a meromorphic function in the whole complex plane with a simple pole at $s=1$, and further that it has a zero at all non-positive even integers, i.e. at $s=0$ and at those negative even integers where the Riemann zeta function has the so-called trivial zeros. As a by-product of the study, both the upper and the lower bounds are also given for the first eigenvalue of the non-commutative harmonic oscillator.
Aspects of non-geometry in string theory

International Nuclear Information System (INIS)

Patalong, Peter

2013-01-01

This thesis investigates various manifestations of non-geometry in string theory. It utilises different frameworks to study how non-geometry appears in the target space, how non-geometry and non-geometric fluxes are interconnected, how non-geometry can be captured in effective field theories and how a possible extension of the standard string worldsheet model can accommodate non-geometric setups. The first part provides an example that non-geometry can imply non-commutativity of the closed string coordinate fields. Three T-dual frames are investigated, the three-torus with constant H-flux, the twisted torus and the torus with non-geometric flux Q. Under the assumption of dilute flux, a mode expansion and the canonical quantisation are carried out in the second case up to linear order in the flux parameter. T-duality is then used to relate the commutators of the string expansion modes to the coordinate field commutator in the non-geometric third frame. Non-commutativity is found and related to the non-geometric flux Q and the string winding, it therefore appears as an intrinsically string theoretic feature. The second part investigates non-geometry in the context of ten-dimensional effective field theories, i.e. double field theory and supergravity. A field redefinition is implemented that takes the form of a T-duality transformation, it reveals an alternative set of field variables allowing to define non-geometric fluxes Q and R in higher dimensions. The perspective of double field theory provides a geometric interpretation of those by taking into account a new type of covariant winding derivative. The perspective of the ten-dimensional supergravity allows to investigate the interplay between non-geometric field configurations and non-geometric fluxes. For the three-torus example, a well-defined action can be found, and a simple dimensional reduction makes contact to the known four-dimensional potential. It thus proves the correct uplift of Q and R to higher
Connes distance function on fuzzy sphere and the connection between geometry and statistics

International Nuclear Information System (INIS)

Devi, Yendrembam Chaoba; Chakraborty, Biswajit; Prajapat, Shivraj; Mukhopadhyay, Aritra K.; Scholtz, Frederik G.

2015-01-01

An algorithm to compute Connes spectral distance, adaptable to the Hilbert-Schmidt operatorial formulation of non-commutative quantum mechanics, was developed earlier by introducing the appropriate spectral triple and used to compute infinitesimal distances in the Moyal plane, revealing a deep connection between geometry and statistics. In this paper, using the same algorithm, the Connes spectral distance has been calculated in the Hilbert-Schmidt operatorial formulation for the fuzzy sphere whose spatial coordinates satisfy the su(2) algebra. This has been computed for both the discrete and the Perelemov’s SU(2) coherent state. Here also, we get a connection between geometry and statistics which is shown by computing the infinitesimal distance between mixed states on the quantum Hilbert space of a particular fuzzy sphere, indexed by n ∈ ℤ/2
Noncommutative Phase Spaces by Coadjoint Orbits Method

Directory of Open Access Journals (Sweden)

Ancille Ngendakumana

2011-12-01

Full Text Available We introduce noncommutative phase spaces by minimal couplings (usual one, dual one and their mixing. We then realize some of them as coadjoint orbits of the anisotropic Newton-Hooke groups in two- and three-dimensional spaces. Through these constructions the positions and the momenta of the phase spaces do not commute due to the presence of a magnetic field and a dual magnetic field.
Newton's second law in a non-commutative space

International Nuclear Information System (INIS)

Romero, Juan M.; Santiago, J.A.; Vergara, J. David

2003-01-01

In this Letter we show that corrections to Newton's second law appear if we assume a symplectic structure consistent with the commutation rules of the non-commutative quantum mechanics. For central field we find that the correction term breaks the rotational symmetry. For the Kepler problem, this term is similar to a Coriolis force
Dispersion relations in the noncommutative φ3 and Wess-Zumino model in the Yang-Feldman formalism

International Nuclear Information System (INIS)

Doescher, C.; Zahn, J.

2006-05-01

We study dispersion relations in the noncommutative φ 3 and Wess-Zumino model in the Yang-Feldman formalism at one-loop order. Non-planar graphs lead to a distortion of the dispersion relation. We find that this effect is small if the scale of noncommutativity is identified with the Planck scale and parameters typical for a Higgs field are employed. (Orig.)
Bootstrapping non-commutative gauge theories from L∞ algebras

Science.gov (United States)

Blumenhagen, Ralph; Brunner, Ilka; Kupriyanov, Vladislav; Lüst, Dieter

2018-05-01

Non-commutative gauge theories with a non-constant NC-parameter are investigated. As a novel approach, we propose that such theories should admit an underlying L∞ algebra, that governs not only the action of the symmetries but also the dynamics of the theory. Our approach is well motivated from string theory. We recall that such field theories arise in the context of branes in WZW models and briefly comment on its appearance for integrable deformations of AdS5 sigma models. For the SU(2) WZW model, we show that the earlier proposed matrix valued gauge theory on the fuzzy 2-sphere can be bootstrapped via an L∞ algebra. We then apply this approach to the construction of non-commutative Chern-Simons and Yang-Mills theories on flat and curved backgrounds with non-constant NC-structure. More concretely, up to the second order, we demonstrate how derivative and curvature corrections to the equations of motion can be bootstrapped in an algebraic way from the L∞ algebra. The appearance of a non-trivial A∞ algebra is discussed, as well.
Duality and noncommutative planes

DEFF Research Database (Denmark)

Jøndrup, Søren

2015-01-01

We study extensions of simple modules over an associative ring A and we prove that for twosided ideals mm and nn with artinian factors the condition ExtA1(A/m,A/n)≠0 holds for the left A -modules A/mA/m and A/nA/n if and only if it holds for the right modules A/nA/n and A/mA/m. The methods pro...... proving this are applied to show that noncommutative models of the plane, i.e. algebras of the form k〈x,y〉/(f)k〈x,y〉/(f), where f∈([x,y])f∈([x,y]) are noetherian only in case (f)=([x,y])...
Effective potential and spontaneous symmetry breaking in the noncommutative φ6 model

International Nuclear Information System (INIS)

Barbosa, G.D.

2004-01-01

We study the conditions for spontaneous symmetry breaking of the (2+1)-dimensional noncommutative φ 6 model in the small-θ limit. In this regime, considering the model as a cutoff theory, it is reasonable to assume translational invariance as a property of the vacuum state and study the conditions for spontaneous symmetry breaking by an effective potential analysis. An investigation of up to the two-loop level reveals that noncommutative effects can modify drastically the shape of the effective potential. Under reasonable conditions, the nonplanar sector of the theory can become dominant and induce symmetry breaking for values of the mass and coupling constants not reached by the commutative counterpart
Wigner Functions for the Bateman System on Noncommutative Phase Space

Science.gov (United States)

Heng, Tai-Hua; Lin, Bing-Sheng; Jing, Si-Cong

2010-09-01

We study an important dissipation system, i.e. the Bateman model on noncommutative phase space. Using the method of deformation quantization, we calculate the Exp functions, and then derive the Wigner functions and the corresponding energy spectra.
Wigner Functions for the Bateman System on Noncommutative Phase Space

International Nuclear Information System (INIS)

Tai-Hua, Heng; Bing-Sheng, Lin; Si-Cong, Jing

2010-01-01

We study an important dissipation system, i.e. the Bateman model on noncommutative phase space. Using the method of deformation quantization, we calculate the Exp functions, and then derive the Wigner functions and the corresponding energy spectra
Gravity's rainbow: A bridge between LQC and DSR

Energy Technology Data Exchange (ETDEWEB)

Gorji, M.A., E-mail: m.gorji@stu.umz.ac.ir [Department of Physics, Faculty of Basic Sciences, University of Mazandaran, P.O. Box 47416-95447, Babolsar (Iran, Islamic Republic of); Nozari, K., E-mail: knozari@umz.ac.ir [Department of Physics, Faculty of Basic Sciences, University of Mazandaran, P.O. Box 47416-95447, Babolsar (Iran, Islamic Republic of); Vakili, B., E-mail: b.vakili@iauctb.ac.ir [Department of Physics, Central Tehran Branch, Islamic Azad University, Tehran (Iran, Islamic Republic of)

2017-02-10

The doubly special relativity (DSR) theories are constructed in order to take into account an observer-independent length scale in special relativity framework. Gravity's rainbow is a simple generalization of DSR theories to incorporate gravity. In this paper, we show that the effective Friedmann equations that are suggested by loop quantum cosmology (LQC) can be exactly reobtained in rainbow cosmology setup. The deformed geometry of LQC then fixes the modified dispersion relation and results in a unique DSR model. In comparison with standard LQC scenario where only the geometry is modified, both geometry and matter parts get modified in our setup. In this respect, we show that the total number of microstates for the universe is finite which suggests the statistical origin of the energy and entropy density bounds. These results explicitly show that the DSR theories are appropriate candidates for the flat limit of loop quantum gravity.
The M5-brane and non-commutative open strings

NARCIS (Netherlands)

Bergshoeff, E.; Berman, D.S.; Schaar, J.P. van der; Sundell, P.

2001-01-01

The M-theory origin of non-commutative open-string theory is examined by investigating the M-theory 5-brane at near critical field strength. In particular, it is argued that the open-membrane metric provides the appropriate moduli when calculating the duality relations between M and II
Moyal noncommutative integrability and the Burgers-KdV mapping

International Nuclear Information System (INIS)

Sedra, M.B.

2005-12-01

The Moyal momentum algebra, is once again used to discuss some important aspects of NC integrable models and 2d conformal field theories. Among the results presented, we set up algebraic structures and makes useful convention notations leading to extract non trivial properties of the Moyal momentum algebra. We study also the Lax pair building mechanism for particular examples namely, the noncommutative KdV and Burgers systems. We show in a crucial step that these two systems are mapped to each other through the following crucial mapping ∂ t 2 → ∂ t 3 ≡ ∂ t 2 ∂ x + α∂ x 3 . This makes a strong constraint on the NC Burgers system which corresponds to linearizing its associated differential equation. From the CFT's point of view, this constraint equation is nothing but the analogue of the conservation law of the conformal current. We believe that the considered mapping might help to bring new insights towards understanding the integrability of noncommutative 2d-systems. (author)
UV / IR mixing in noncommutative field theory via open string loops

International Nuclear Information System (INIS)

Kiem, Youngjai; Lee, Sangmin

2000-01-01

We explicitly evaluate one-loop (annulus) planar and nonplanar open string amplitudes in the presence of the background NS-NS two-form field. In the decoupling limit of Seiberg and Witten, we find that the nonplanar string amplitudes reproduce the UV/IR mixing of noncommutative field theories. In particular, the investigation of the UV regime of the open string amplitudes shows that certain IR closed string degrees of freedom survive the decoupling limit as previously predicted from the noncommutative field theory analysis. These degrees of freedom are responsible for the quadratic, linear and logarithmic IR singularities when the D-branes embedded in space-time have the codimension zero, one and two, respectively. The analysis is given for both bosonic and supersymmetric open strings
A strong astrophysical constraint on the violation of special relativity by quantum gravity.

Science.gov (United States)

Jacobson, T; Liberati, S; Mattingly, D

2003-08-28

Special relativity asserts that physical phenomena appear the same to all unaccelerated observers. This is called Lorentz symmetry and relates long wavelengths to short ones: if the symmetry is exact it implies that space-time must look the same at all length scales. Several approaches to quantum gravity, however, suggest that there may be a microscopic structure of space-time that leads to a violation of Lorentz symmetry. This might arise because of the discreteness or non-commutivity of space-time, or through the action of extra dimensions. Here we determine a very strong constraint on a type of Lorentz violation that produces a maximum electron speed less than the speed of light. We use the observation of 100-MeV synchrotron radiation from the Crab nebula to improve the previous limit by a factor of 40 million, ruling out this type of Lorentz violation, and thereby providing an important constraint on theories of quantum gravity.
Review of lattice supersymmetry and gauge-gravity duality

International Nuclear Information System (INIS)

Joseph, Anosh

2015-12-01

We review the status of recent investigations on validating the gauge-gravity duality conjecture through numerical simulations of strongly coupled maximally supersymmetric thermal gauge theories. In the simplest setting, the gauge-gravity duality connects systems of D0-branes and black hole geometries at finite temperature to maximally supersymmetric gauged quantum mechanics at the same temperature. Recent simulations show that non-perturbative gauge theory results give excellent agreement with the quantum gravity predictions, thus proving strong evidence for the validity of the duality conjecture and more insight into quantum black holes and gravity.
Topology and geometry for physicists

CERN Document Server

Nash, Charles

1983-01-01

Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. ""Thoroughly recommended"" by The Physics Bulletin, this volume's physics applications range fr
Three theorems on near horizon extremal vanishing horizon geometries

Directory of Open Access Journals (Sweden)

S. Sadeghian

2016-02-01

Full Text Available EVH black holes are Extremal black holes with Vanishing Horizon area, where vanishing of horizon area is a result of having a vanishing one-cycle on the horizon. We prove three theorems regarding near horizon geometry of EVH black hole solutions to generic Einstein gravity theories in diverse dimensions. These generic gravity theories are Einstein–Maxwell-dilaton-Λ theories, and gauged or ungauged supergravity theories with U(1 Maxwell fields. Our three theorems are: (1 The near horizon geometry of any EVH black hole has a three dimensional maximally symmetric subspace. (2 If the energy momentum tensor of the theory satisfies strong energy condition either this 3d part is an AdS3, or the solution is a direct product of a locally 3d flat space and a d−3 dimensional part. (3 These results extend to the near horizon geometry of near-EVH black holes, for which the AdS3 part is replaced with BTZ geometry.

Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions

Directory of Open Access Journals (Sweden)

Derek K. Wise

2009-08-01

Full Text Available Einstein gravity in both 3 and 4 dimensions, as well as some interesting generalizations, can be written as gauge theories in which the connection is a Cartan connection for geometry modeled on a symmetric space. The relevant models in 3 dimensions include Einstein gravity in Chern-Simons form, as well as a new formulation of topologically massive gravity, with arbitrary cosmological constant, as a single constrained Chern-Simons action. In 4 dimensions the main model of interest is MacDowell-Mansouri gravity, generalized to include the Immirzi parameter in a natural way. I formulate these theories in Cartan geometric language, emphasizing also the role played by the symmetric space structure of the model. I also explain how, from the perspective of these Cartan-geometric formulations, both the topological mass in 3d and the Immirzi parameter in 4d are the result of non-simplicity of the Lorentz Lie algebra so(3,1 and its relatives. Finally, I suggest how the language of Cartan geometry provides a guiding principle for elegantly reformulating any 'gauge theory of geometry'.
Quadratic algebras in the noncommutative integration method of wave equation

International Nuclear Information System (INIS)

Varaksin, O.L.

1995-01-01

The paper deals with the investigation of applications of the method of noncommutative integration of linear differential equations by partial derivatives. Nontrivial example was taken for integration of three-dimensions wave equation with the use of non-Abelian quadratic algebras
quasi hyperrigidity and weak peak points for non-commutative ...

Indian Academy of Sciences (India)

7

Abstract. In this article, we introduce the notions of weak boundary repre- sentation, quasi hyperrigidity and weak peak points in the non-commutative setting for operator systems in C∗-algebras. An analogue of Saskin's theorem relating quasi hyperrigidity and weak Choquet boundary for particular classes of C∗-algebras is ...
Quantum gravity from descriptive set theory

International Nuclear Information System (INIS)

El Naschie, M.S.

2004-01-01

We start from Hilbert's criticism of the axioms of classical geometry and the possibility of abandoning the Archimedean axiom. Subsequently we proceed to the physical possibility of a fundamental limitation on the smallest length connected to certain singular points in spacetime and below which measurements become meaningless, Finally we arrive at the conclusion that maximising the Hawking-Bekenstein informational content of spacetime makes the existence of a transfinite geometry for physical 'spacetime' not only plausible but probably inevitable. The main part of the paper is then concerned with a proposal for a mathematical description of a transfinite, non-Archimedean geometry using descriptive set theory. Nevertheless, and despite all abstract mathematics, we remain quite close to similar lines of investigation initiated by physicists like A. Wheeler, D. Finkelstein and G. 'tHooft. In particular we introduce a logarithmic gauge transformation linking classical gravity with the electro weak via a version of informational entropy. That way we may claim to have accomplished an important step towards a general theory of quantum gravity using ε (∞) and complexity theory and finding that α G =(2) α-bar ew -1 congruent with (1.7)(10) 38 where α G is the dimensionless Newton gravity constant, and α ew ≅128 is the fine structure constant at the electro weak scale
Metamaterials mimicking dynamic spacetime, D-brane and noncommutativity in string theory

International Nuclear Information System (INIS)

Miao Rongxin; Zheng Rui; Li Miao

2011-01-01

We propose a scheme to mimic the expanding cosmos in 1+2 dimensions in laboratory. Furthermore, we develop a general procedure to use nonlinear metamaterials to mimic D-brane and noncommutativity in string theory.
On 3d bulk geometry of Virasoro coadjoint orbits: orbit invariant charges and Virasoro hair on locally AdS{sub 3} geometries

Energy Technology Data Exchange (ETDEWEB)

Sheikh-Jabbari, M.M. [Institute for Research in Fundamental Sciences (IPM), School of Physics, Tehran (Iran, Islamic Republic of); Yavartanoo, H. [Institute of Theoretical Physics, Chinese Academy of Sciences, State Key Laboratory of Theoretical Physics, Beijing (China)

2016-09-15

Expanding upon [arXiv:1404.4472, arXiv:1511.06079], we provide a further detailed analysis of Banados geometries, the most general solutions to the AdS{sub 3} Einstein gravity with Brown-Henneaux boundary conditions. We analyze in some detail the causal, horizon, and boundary structure, and the geodesic motion on these geometries, as well as the two classes of symplectic charges one can associate with these geometries: charges associated with the exact symmetries and the Virasoro charges. We elaborate on the one-to-one relation between the coadjoint orbits of two copies of the Virasoro group and Banados geometries. We discuss that the information as regards the Banados geometries falls into two categories: ''orbit invariant'' information and ''Virasoro hairs''. The former concerns geometric quantities, while the latter are specified by the non-local surface integrals. We elaborate on multi-BTZ geometries which have a number of disconnected pieces at the horizon bifurcation curve. We study multi-BTZ black hole thermodynamics and discuss that the thermodynamic quantities are orbit invariants. We also comment on the implications of our analysis for a 2d CFT dual which could possibly be dual to AdS{sub 3} Einstein gravity. (orig.)
Magnetic branes in Gauss-Bonnet gravity with nonlinear electrodynamics: correction of magnetic branes in Einstein-Maxwell gravity

Energy Technology Data Exchange (ETDEWEB)

Hendi, Seyed Hossein [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); Panahiyan, Shahram; Panah, Behzad Eslam [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of)

2015-06-15

In this paper, we consider two first order corrections to both the gravity and the gauge sides of the Einstein-Maxwell gravity: Gauss-Bonnet gravity and quadratic Maxwell invariant as corrections. We obtain horizonless magnetic solutions by implying a metric representing a topological defect. We analyze the geometric properties of the solutions and investigate the effects of both corrections, and find that these solutions may be interpreted as magnetic branes. We study the singularity condition and find a nonsingular spacetime with a conical geometry. We also investigate the effects of different parameters on the deficit angle of spacetime near the origin. (orig.)
Magnetic branes in Gauss-Bonnet gravity with nonlinear electrodynamics: correction of magnetic branes in Einstein-Maxwell gravity

International Nuclear Information System (INIS)

Hendi, Seyed Hossein; Panahiyan, Shahram; Panah, Behzad Eslam

2015-01-01

In this paper, we consider two first order corrections to both the gravity and the gauge sides of the Einstein-Maxwell gravity: Gauss-Bonnet gravity and quadratic Maxwell invariant as corrections. We obtain horizonless magnetic solutions by implying a metric representing a topological defect. We analyze the geometric properties of the solutions and investigate the effects of both corrections, and find that these solutions may be interpreted as magnetic branes. We study the singularity condition and find a nonsingular spacetime with a conical geometry. We also investigate the effects of different parameters on the deficit angle of spacetime near the origin. (orig.)
Wigner functions for noncommutative quantum mechanics: A group representation based construction

Energy Technology Data Exchange (ETDEWEB)

Chowdhury, S. Hasibul Hassan, E-mail: shhchowdhury@gmail.com [Chern Institute of Mathematics, Nankai University, Tianjin 300071 (China); Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8 (Canada); Ali, S. Twareque, E-mail: twareque.ali@concordia.ca [Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8 (Canada)

2015-12-15

This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantum mechanics, their marginal distributions, and star-products, following a technique developed earlier, viz, using the unitary irreducible representations of the group G{sub NC}, which is the three fold central extension of the Abelian group of ℝ{sup 4}. These representations have been exhaustively studied in earlier papers. The group G{sub NC} is identified with the kinematical symmetry group of noncommutative quantum mechanics of a system with two degrees of freedom. The Wigner functions studied here reflect different levels of non-commutativity—both the operators of position and those of momentum not commuting, the position operators not commuting and finally, the case of standard quantum mechanics, obeying the canonical commutation relations only.
Quantum group structure and local fields in the algebraic approach to 2D gravity

CERN Document Server

Schnittger, Jens

1994-01-01

This review contains a summary of work by J.-L. Gervais and the author on the operator approach to 2d gravity. Special emphasis is placed on the construction of local observables -the Liouville exponentials and the Liouville field itself - and the underlying algebra of chiral vertex operators. The double quantum group structure arising from the presence of two screening charges is discussed and the generalized algebra and field operators are derived. In the last part, we show that our construction gives rise to a natural definition of a quantum tau function, which is a noncommutative version of the classical group-theoretic representation of the Liouville fields by Leznov and Saveliev.
Gravity duals of supersymmetric gauge theories on three-manifolds

International Nuclear Information System (INIS)

Farquet, Daniel; Lorenzen, Jakob; Martelli, Dario; Sparks, James

2016-01-01

We study gravity duals to a broad class of N=2 supersymmetric gauge theories defined on a general class of three-manifold geometries. The gravity backgrounds are based on Euclidean self-dual solutions to four-dimensional gauged supergravity. As well as constructing new examples, we prove in general that for solutions defined on the four-ball the gravitational free energy depends only on the supersymmetric Killing vector, finding a simple closed formula when the solution has U(1)×U(1) symmetry. Our result agrees with the large N limit of the free energy of the dual gauge theory, computed using localization. This constitutes an exact check of the gauge/gravity correspondence for a very broad class of gauge theories with a large N limit, defined on a general class of background three-manifold geometries.
A noncommutative convexity in C*-bimodules

Directory of Open Access Journals (Sweden)

Mohsen Kian

2017-02-01

Full Text Available Let A and B be C*-algebras. We consider a noncommutative convexity in Hilbert A-B-bimodules, called A-B-convexity, as a generalization of C*-convexity in C*-algebras. We show that if X is a Hilbert A-B-bimodule, then Mn(X is a Hilbert Mn(A-Mn(B-bimodule and apply it to show that the closed unit ball of every Hilbert A-B-bimodule is A-B-convex. Some properties of this kind of convexity and various examples have been given.
New effective coupled F((4)R, φ) modified gravity from f((5)R) gravity in five dimensions

International Nuclear Information System (INIS)

Madriz Aguilar, Jose Edgar

2015-01-01

Using some ideas of the Wesson induced matter theory, we obtain a new kind of F( (4) R, φ) modified gravity theory as an effective four-dimensional (4D) theory derived from f( (5) R) gravity in five dimensions (5D). This new theory exhibits a different matter coupling than the one in BBHL theory. We show that the field equations of the Wesson induced matter theory and of some brane-world scenarios can be obtained as maximally symmetric solutions of the same f( (5) R) theory. We found criteria for the Dolgov-Kawasaki instabilities for both the f( (5) R) and the F( (4) R, φ) theories. We demonstrate that under certain conditions imposed on the 5D geometry it is possible to interpret the F( (4) R, φ) theory as a modified gravity theory with dynamical coefficients, making this new theory a viable candidate to address the present accelerating cosmic expansion issue. Matter sources in the F( (4) R, φ) case appear induced by the 5D geometry without the necessity of the introduction of matter sources in 5D. (orig.)
Coproduct and star product in field theories on Lie-algebra noncommutative space-times

International Nuclear Information System (INIS)

Amelino-Camelia, Giovanni; Arzano, Michele

2002-01-01

We propose a new approach to field theory on κ-Minkowski noncommutative space-time, a popular example of Lie-algebra space-time. Our proposal is essentially based on the introduction of a star product, a technique which is proving to be very fruitful in analogous studies of canonical noncommutative space-times, such as the ones recently found to play a role in the description of certain string-theory backgrounds. We find to be incorrect the expectation, previously reported in the literature, that the lack of symmetry of the κ-Poincare coproduct should lead to interaction vertices that are not symmetric under exchanges of the momenta of identical particles entering the relevant processes. We show that in κ-Minkowski the coproduct and the star product must indeed treat momenta in a nonsymmetric way, but the overall structure of interaction vertices is symmetric under exchange of identical particles. We also show that in κ-Minkowski field theories it is convenient to introduce the concepts of 'planar' and 'nonplanar' Feynman loop diagrams, again in close analogy with the corresponding concepts previously introduced in the study of field theories in canonical noncommutative space-times
Effect of roughness and porosity on geometry and kinematics of lock-exchange gravity currents

Science.gov (United States)

Gatto, Elena; Adduce, Claudia; Ferreira, Rui M. L.

2017-04-01

Gravity currents generated by lock-exchange are an important research tool to understand key features of flows driven by a density may be naturally caused by interaction of geophysical nature but may also be triggered by adverse anthropic actions, from oil spills to pollution related turbidity. Research on the fundamental geometrical and kinematic features of these currents is still necessary, especially when they propagate on complex geometries. The purpose of this work is to investigate the shape and the velocity of propagation of gravity currents over rough beds and over rough-porous beds. To attain this objective, different initial conditions were specified, namely smooth bed, rough bed composed of a single layer of 2 mm glass beads and rough and porous bed composed of 4 layers of the same beads. The dimensions of the channel are 300 × 19,6 × 40 cm in which a steel gate is inserted to define the lock. Two initial mixtures were tested: 1015 and 1030 kgm-3. The density is measured with a pycnometer on a high precision balance. The mixture is composed of fresh water, salt and rhodamine, to allow for visualization and measurements based on image analysis. A high-speed video system camera was used to record the motion of the current. The camera has a 50 mm lens and a sampling frequency of 100 fps. Gray-level images were obtained with 8 bit depth. Calibration of gray-levels was performed pixel by pixel to mixture concentrations. The current is examined in three positions: immediately after the gate ((x-x0)/x0 = 0 to 3), in the middle ((x-x0)/x0 = 5 to 8) and at the end of the channel((x - x0)/x0 = 10 to 13). It is shown that the celerity of the gravity current wave front varies with the different boundary conditions. Indeed, the current is faster for the smooth bed and slower for the rough bed conditions. No appreciable effects of porosity were registered on the wave celerity. The shape of the current varied slightly between the rough and the porous-rough tests
Carroll versus Galilei gravity

Energy Technology Data Exchange (ETDEWEB)

Bergshoeff, Eric [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Gomis, Joaquim [Departament de Física Cuàntica i Astrofísica and Institut de Ciències del Cosmos,Universitat de Barcelona,Martí i Franquès 1, E-08028 Barcelona (Spain); Rollier, Blaise [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Rosseel, Jan [Faculty of Physics, University of Vienna,Boltzmanngasse 5, A-1090 Vienna (Austria); Veldhuis, Tonnis ter [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands)

2017-03-30

We consider two distinct limits of General Relativity that in contrast to the standard non-relativistic limit can be taken at the level of the Einstein-Hilbert action instead of the equations of motion. One is a non-relativistic limit and leads to a so-called Galilei gravity theory, the other is an ultra-relativistic limit yielding a so-called Carroll gravity theory. We present both gravity theories in a first-order formalism and show that in both cases the equations of motion (i) lead to constraints on the geometry and (ii) are not sufficient to solve for all of the components of the connection fields in terms of the other fields. Using a second-order formalism we show that these independent components serve as Lagrange multipliers for the geometric constraints we found earlier. We point out a few noteworthy differences between Carroll and Galilei gravity and give some examples of matter couplings.
An introduction to quantum groups and non-commutative differential calculus

International Nuclear Information System (INIS)

Azcarraga, J.A. de; Rodenas, F.

1995-01-01

An introduction to quantum groups and quantum spaces is presented, and the non-commutative calculus on them is discussed. The case of q-Minkowski space is presented as an illustrative example. A set of useful expressions and formulae are collected in an appendix. 45 refs
Towards a theory of nonassociative gravity

International Nuclear Information System (INIS)

Blumenhagen, Ralph; Fuchs, Michael

2016-01-01

Violating the strong constraint of double field theory, non-geometric fluxes were argued to give rise to noncommutative/nonassociative structures. We derive in a rather pedestrian physicist way a differential geometry on the simplest nonassociative (phase-)space arising for a constant non-geometric R-flux. This provides a complementary presentation to the quasi-Hopf representation categorial one delivered by Barnes, Schenkel, Szabo in http://arxiv.org/abs/1409.6331 + http://arxiv.org/abs/1507.02792. As there, the notions of tensors, covariant derivative, torsion and curvature find a star-generalization. We continue the construction with the introduction of a star-metric and its star-inverse where, due to the nonassociativity, we encounter major deviations from the familiar structure. Comments on the Levi-Civita connection, a star-Einstein-Hilbert action and the relation to string theory are included, as well.
Exact BPS bound for noncommutative baby Skyrmions

International Nuclear Information System (INIS)

Domrin, Andrei; Lechtenfeld, Olaf; Linares, Román; Maceda, Marco

2013-01-01

The noncommutative baby Skyrme model is a Moyal deformation of the two-dimensional sigma model plus a Skyrme term, with a group-valued or Grassmannian target. Exact abelian solitonic solutions have been identified analytically in this model, with a singular commutative limit. Inside any given Grassmannian, we establish a BPS bound for the energy functional, which is saturated by these baby Skyrmions. This asserts their stability for unit charge, as we also test in second-order perturbation theory
Faddeev–Jackiw quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions

Energy Technology Data Exchange (ETDEWEB)

Escalante, Alberto, E-mail: aescalan@ifuap.buap.mx; Manuel-Cabrera, J., E-mail: jmanuel@ifuap.buap.mx

2015-10-15

A detailed Faddeev–Jackiw quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions is performed. We obtain for the theories under study the constraints, the gauge transformations, the generalized Faddeev–Jackiw brackets and we perform the counting of physical degrees of freedom. In addition, we compare our results with those found in the literature where the canonical analysis is developed, in particular, we show that both the generalized Faddeev–Jackiw brackets and Dirac’s brackets coincide to each other. Finally we discuss some remarks and prospects. - Highlights: • A detailed Faddeev–Jackiw analysis for exotic action of gravity is performed. • We show that Dirac’s brackets and Generalized [FJ] brackets are equivalent. • Without fixing the gauge exotic action is a non-commutative theory. • The fundamental gauge transformations of the theory are found. • Dirac and Faddeev–Jackiw approaches are compared.

A noncommutative mean ergodic theorem for partial W*-dynamical semigroups

International Nuclear Information System (INIS)

Ekhaguere, G.O.S.

1992-12-01

A noncommutative mean ergodic theorem for dynamical semigroups of maps on partial W*-algebras of linear operators from a pre-Hilbert space into its completion is proved. This generalizes a similar result of Watanabe for dynamical semigroups of maps on W*-algebras of operators. (author). 14 refs
The Finsler spacetime framework. Backgrounds for physics beyond metric geometry

International Nuclear Information System (INIS)

Pfeifer, Christian

2013-11-01

The fundamental structure on which physics is described is the geometric spacetime background provided by a four dimensional manifold equipped with a Lorentzian metric. Most importantly the spacetime manifold does not only provide the stage for physical field theories but its geometry encodes causality, observers and their measurements and gravity simultaneously. This threefold role of the Lorentzian metric geometry of spacetime is one of the key insides of general relativity. During this thesis we extend the background geometry for physics from the metric framework of general relativity to our Finsler spacetime framework and ensure that the threefold role of the geometry of spacetime in physics is not changed. The geometry of Finsler spacetimes is determined by a function on the tangent bundle and includes metric geometry. In contrast to the standard formulation of Finsler geometry our Finsler spacetime framework overcomes the differentiability and existence problems of the geometric objects in earlier attempts to use Finsler geometry as an extension of Lorentzian metric geometry. The development of our nonmetric geometric framework which encodes causality is one central achievement of this thesis. On the basis of our well-defined Finsler spacetime geometry we are able to derive dynamics for the non-metric Finslerian geometry of spacetime from an action principle, obtained from the Einstein-Hilbert action, for the first time. We can complete the dynamics to a non-metric description of gravity by coupling matter fields, also formulated via an action principle, to the geometry of our Finsler spacetimes. We prove that the combined dynamics of the fields and the geometry are consistent with general relativity. Furthermore we demonstrate how to define observers and their measurements solely through the non-metric spacetime geometry. Physical consequence derived on the basis of our Finsler spacetime are: a possible solution to the fly-by anomaly in the solar system; the
The Finsler spacetime framework. Backgrounds for physics beyond metric geometry

Energy Technology Data Exchange (ETDEWEB)

Pfeifer, Christian

2013-11-15

The fundamental structure on which physics is described is the geometric spacetime background provided by a four dimensional manifold equipped with a Lorentzian metric. Most importantly the spacetime manifold does not only provide the stage for physical field theories but its geometry encodes causality, observers and their measurements and gravity simultaneously. This threefold role of the Lorentzian metric geometry of spacetime is one of the key insides of general relativity. During this thesis we extend the background geometry for physics from the metric framework of general relativity to our Finsler spacetime framework and ensure that the threefold role of the geometry of spacetime in physics is not changed. The geometry of Finsler spacetimes is determined by a function on the tangent bundle and includes metric geometry. In contrast to the standard formulation of Finsler geometry our Finsler spacetime framework overcomes the differentiability and existence problems of the geometric objects in earlier attempts to use Finsler geometry as an extension of Lorentzian metric geometry. The development of our nonmetric geometric framework which encodes causality is one central achievement of this thesis. On the basis of our well-defined Finsler spacetime geometry we are able to derive dynamics for the non-metric Finslerian geometry of spacetime from an action principle, obtained from the Einstein-Hilbert action, for the first time. We can complete the dynamics to a non-metric description of gravity by coupling matter fields, also formulated via an action principle, to the geometry of our Finsler spacetimes. We prove that the combined dynamics of the fields and the geometry are consistent with general relativity. Furthermore we demonstrate how to define observers and their measurements solely through the non-metric spacetime geometry. Physical consequence derived on the basis of our Finsler spacetime are: a possible solution to the fly-by anomaly in the solar system; the
Topspin networks in loop quantum gravity

International Nuclear Information System (INIS)

Duston, Christopher L

2012-01-01

We discuss the extension of loop quantum gravity to topspin networks, a proposal which allows topological information to be encoded in spin networks. We will show that this requires minimal changes to the phase space, C*-algebra and Hilbert space of cylindrical functions. We will also discuss the area and Hamiltonian operators, and show how they depend on the topology. This extends the idea of ‘background independence’ in loop quantum gravity to include topology as well as geometry. It is hoped this work will confirm the usefulness of the topspin network formalism and open up several new avenues for research into quantum gravity. (paper)
The relation between Euclidean and Lorentzian 2D quantum gravity

NARCIS (Netherlands)

Ambjørn, J.; Correia, J.; Kristjansen, C.; Loll, R.

1999-01-01

Starting from 2D Euclidean quantum gravity, we show that one recovers 2D Lorentzian quantum gravity by removing all baby universes. Using a peeling procedure to decompose the discrete, triangulated geometries along a one-dimensional path, we explicitly associate with each Euclidean space-time a
Quadratic algebras applied to noncommutative integration of the Klein-Gordon equation: Four-dimensional quadratic algebras containing three-dimensional nilpotent lie algebras

International Nuclear Information System (INIS)

Varaksin, O.L.; Firstov, V.V.; Shapovalov, A.V.

1995-01-01

The study is continued on noncommutative integration of linear partial differential equations in application to the exact integration of quantum-mechanical equations in a Riemann space. That method gives solutions to the Klein-Gordon equation when the set of noncommutative symmetry operations for that equation forms a quadratic algebra consisting of one second-order operator and of first-order operators forming a Lie algebra. The paper is a continuation of, where a single nontrivial example is used to demonstrate noncommutative integration of the Klein-Gordon equation in a Riemann space not permitting variable separation
General classical solutions in the noncommutative CPN-1 model

International Nuclear Information System (INIS)

Foda, O.; Jack, I.; Jones, D.R.T.

2002-01-01

We give an explicit construction of general classical solutions for the noncommutative CP N-1 model in two dimensions, showing that they correspond to integer values for the action and topological charge. We also give explicit solutions for the Dirac equation in the background of these general solutions and show that the index theorem is satisfied
Imaging multipole gravity anomaly sources by 3D probability tomography

International Nuclear Information System (INIS)

Alaia, Raffaele; Patella, Domenico; Mauriello, Paolo

2009-01-01

We present a generalized theory of the probability tomography applied to the gravity method, assuming that any Bouguer anomaly data set can be caused by a discrete number of monopoles, dipoles, quadrupoles and octopoles. These elementary sources are used to characterize, in an as detailed as possible way and without any a priori assumption, the shape and position of the most probable minimum structure of the gravity sources compatible with the observed data set, by picking out the location of their centres and peculiar points of their boundaries related to faces, edges and vertices. A few synthetic examples using simple geometries are discussed in order to demonstrate the notably enhanced resolution power of the new approach, compared with a previous formulation that used only monopoles and dipoles. A field example related to a gravity survey carried out in the volcanic area of Mount Etna (Sicily, Italy) is presented, aimed at imaging the geometry of the minimum gravity structure down to 8 km of depth bsl
A Note on UV/IR Mixing and Non-Commutative Instanton Calculus

CERN Document Server

Bichl, A A

2003-01-01

We estimate the instanton-induced vacuum energy in non-commutative U(1) Yang-Mills theory in four dimensions. In the dilute gas approximation, it is found to be plagued by infrared divergences, as a result of UV/IR mixing.
Gravity from entanglement and RG flow in a top-down approach

Science.gov (United States)

Kwon, O.-Kab; Jang, Dongmin; Kim, Yoonbai; Tolla, D. D.

2018-05-01

The duality between a d-dimensional conformal field theory with relevant deformation and a gravity theory on an asymptotically AdS d+1 geometry, has become a suitable tool in the investigation of the emergence of gravity from quantum entanglement in field theory. Recently, we have tested the duality between the mass-deformed ABJM theory and asymptotically AdS4 gravity theory, which is obtained from the KK reduction of the 11-dimensional supergravity on the LLM geometry. In this paper, we extend the KK reduction procedure beyond the linear order and establish non-trivial KK maps between 4-dimensional fields and 11-dimensional fluctuations. We rely on this gauge/gravity duality to calculate the entanglement entropy by using the Ryu-Takayanagi holographic formula and the path integral method developed by Faulkner. We show that the entanglement entropies obtained using these two methods agree when the asymptotically AdS4 metric satisfies the linearized Einstein equation with nonvanishing energy-momentum tensor for two scalar fields. These scalar fields encode the information of the relevant deformation of the ABJM theory. This confirms that the asymptotic limit of LLM geometry is the emergent gravity of the quantum entanglement in the mass-deformed ABJM theory with a small mass parameter. We also comment on the issue of the relative entropy and the Fisher information in our setup.
What goes up... gravity and scientific method

CERN Document Server

Kosso, Peter

2017-01-01

The concept of gravity provides a natural phenomenon that is simultaneously obvious and obscure; we all know what it is, but rarely question why it is. The simple observation that 'what goes up must come down' contrasts starkly with our current scientific explanation of gravity, which involves challenging and sometimes counterintuitive concepts. With such extremes between the plain and the perplexing, gravity forces a sharp focus on scientific method. Following the history of gravity from Aristotle to Einstein, this clear account highlights the logic of scientific method for non-specialists. Successive theories of gravity and the evidence for each are presented clearly and rationally, focusing on the fundamental ideas behind them. Using only high-school level algebra and geometry, the author emphasizes what the equations mean rather than how they are derived, making this accessible for all those curious about gravity and how science really works.
Topology Change and the Emergence of Geometry in Two Dimensional Causal Quantum Gravity

NARCIS (Netherlands)

Westra, W.

2007-01-01

Despite many attempts, gravity has vigorously resisted a unification with the laws of quantum mechanics. Besides a plethora of technical issues, one is also faced with many interesting conceptual problems. The study of quantum gravity in lower dimensional models ameliorates the technical
Hawking, fiducial, and free-fall temperature of black hole on gravity's rainbow

Energy Technology Data Exchange (ETDEWEB)

Gim, Yongwan; Kim, Wontae [Sogang University, Department of Physics, Seoul (Korea, Republic of)

2016-03-15

On gravity's rainbow, the energy of test particles deforms the geometry of a black hole in such a way that the corresponding Hawking temperature is expected to be modified. It means that the fiducial and free-fall temperatures on the black hole background should also be modified according to deformation of the geometry. In this work, the probing energy of test particles is assumed as the average energy of the Hawking particle in order to study the particle back reaction of the geometry by using the advantage of gravity's rainbow. We shall obtain the modified fiducial and free-fall temperatures, respectively. The behaviors of these two temperatures on the horizon tell us that black hole complementarity is still well defined on gravity's rainbow. (orig.)
Notes on algebraic invariants for non-commutative dynamical systems

Energy Technology Data Exchange (ETDEWEB)

Longo, R [Rome Univ. (Italy). Istituto di Matematica

1979-11-01

We consider an algebraic invariant for non-commutative dynamical systems naturally arising as the spectrum of the modular operator associated to an invariant state, provided certain conditions of mixing type are present. This invariant turns out to be exactly the annihilator of the invariant T of Connes. Further comments are included, in particular on the type of certain algebras of local observables
Massive neutrinos in almost-commutative geometry

International Nuclear Information System (INIS)

Stephan, Christoph A.

2007-01-01

In the noncommutative formulation of the standard model of particle physics by Chamseddine and Connes [Commun. Math. Phys. 182, 155 (1996), e-print hep-th/9606001], one of the three generations of fermions has to possess a massless neutrino. [C. P. Martin et al., Phys. Rep. 29, 363 (1998), e-print hep-th-9605001]. This formulation is consistent with neutrino oscillation experiments and the known bounds of the Pontecorvo-Maki-Nakagawa-Sakata matrix (PMNS matrix). But future experiments which may be able to detect neutrino masses directly and high-precision measurements of the PMNS matrix might need massive neutrinos in all three generations. In this paper we present an almost-commutative geometry which allows for a standard model with massive neutrinos in all three generations. This model does not follow in a straightforward way from the version of Chamseddine and Connes since it requires an internal algebra with four summands of matrix algebras, instead of three summands for the model with one massless neutrino
Time machines and traversable wormholes in modified theories of gravity

Directory of Open Access Journals (Sweden)

Lobo Francisco S.N.

2013-09-01

Full Text Available We review recent work on wormhole geometries in the context of modified theories of gravity, in particular, in f(R gravity and with a nonminimal curvature-matter coupling, and in the recently proposed hybrid metric-Palatini theory. In principle, the normal matter threading the throat can be shown to satisfy the energy conditions and it is the higher order curvatures terms that sustain these wormhole geometries. We also briefly review the conversion of wormholes into time-machines, explore several of the time travel paradoxes and possible remedies to these intriguing side-effects in wormhole physics.
Area-preserving diffeomorphisms in gauge theory on a non-commutative plane. A lattice study

International Nuclear Information System (INIS)

Bietenholz, W.; Bigarini, A.; INFN, Sezione di Perugia; Humboldt-Universitaet, Berlin; Torrielli, A.

2007-06-01

We consider Yang-Mills theory with the U(1) gauge group on a non-commutative plane. Perturbatively it was observed that the invariance of this theory under area-preserving diffeomorphisms (APDs) breaks down to a rigid subgroup SL(2,R). Here we present explicit results for the APD symmetry breaking at finite gauge coupling and finite non-commutativity. They are based on lattice simulations and measurements of Wilson loops with the same area but with a variety of different shapes. Our results confirm the expected loss of invariance under APDs. Moreover, they strongly suggest that non-perturbatively the SL(2,R) symmetry does not persist either. (orig.)
Remarks on twisted noncommutative quantum field theory

Energy Technology Data Exchange (ETDEWEB)

Zahn, J. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

2006-04-15

We review recent results on twisted noncommutative quantum field theory by embedding it into a general framework for the quantization of systems with a twisted symmetry. We discuss commutation relations in this setting and show that the twisted structure is so rigid that it is hard to derive any predictions, unless one gives up general principles of quantum theory. It is also shown that the twisted structure is not responsible for the presence or absence of UV/IR-mixing, as claimed in the literature. (Orig.)
Quantum group structure and local fields in the algebraic approach to 2D gravity

Science.gov (United States)

Schnittger, J.

1995-07-01

This review contains a summary of the work by J.-L. Gervais and the author on the operator approach to 2d gravity. Special emphasis is placed on the construction of local observables — the Liouville exponentials and the Liouville field itself — and the underlying algebra of chiral vertex operators. The double quantum group structure arising from the presence of two screening charges is discussed and the generalized algebra and field operators are derived. In the last part, we show that our construction gives rise to a natural definition of a quantum tau function, which is a noncommutative version of the classical group-theoretic representation of the Liouville fields by Leznov and Saveliev.
Group theoretical construction of planar noncommutative phase spaces

Energy Technology Data Exchange (ETDEWEB)

Ngendakumana, Ancille, E-mail: nancille@yahoo.fr; Todjihoundé, Leonard, E-mail: leonardt@imsp.uac.org [Institut de Mathématiques et des Sciences Physiques (IMSP), Porto-Novo (Benin); Nzotungicimpaye, Joachim, E-mail: kimpaye@kie.ac.rw [Kigali Institute of Education (KIE), Kigali (Rwanda)

2014-01-15

Noncommutative phase spaces are generated and classified in the framework of centrally extended anisotropic planar kinematical Lie groups as well as in the framework of noncentrally abelian extended planar absolute time Lie groups. Through these constructions the coordinates of the phase spaces do not commute due to the presence of naturally introduced fields giving rise to minimal couplings. By symplectic realizations methods, physical interpretations of generators coming from the obtained structures are given.

Group theoretical construction of planar noncommutative phase spaces

International Nuclear Information System (INIS)

Ngendakumana, Ancille; Todjihoundé, Leonard; Nzotungicimpaye, Joachim

2014-01-01

Noncommutative phase spaces are generated and classified in the framework of centrally extended anisotropic planar kinematical Lie groups as well as in the framework of noncentrally abelian extended planar absolute time Lie groups. Through these constructions the coordinates of the phase spaces do not commute due to the presence of naturally introduced fields giving rise to minimal couplings. By symplectic realizations methods, physical interpretations of generators coming from the obtained structures are given
Warped conformal field theory as lower spin gravity

Science.gov (United States)

Hofman, Diego M.; Rollier, Blaise

2015-08-01

Two dimensional Warped Conformal Field Theories (WCFTs) may represent the simplest examples of field theories without Lorentz invariance that can be described holographically. As such they constitute a natural window into holography in non-AdS space-times, including the near horizon geometry of generic extremal black holes. It is shown in this paper that WCFTs posses a type of boost symmetry. Using this insight, we discuss how to couple these theories to background geometry. This geometry is not Riemannian. We call it Warped Geometry and it turns out to be a variant of a Newton-Cartan structure with additional scaling symmetries. With this formalism the equivalent of Weyl invariance in these theories is presented and we write two explicit examples of WCFTs. These are free fermionic theories. Lastly we present a systematic description of the holographic duals of WCFTs. It is argued that the minimal setup is not Einstein gravity but an SL (2, R) × U (1) Chern-Simons Theory, which we call Lower Spin Gravity. This point of view makes manifest the definition of boundary for these non-AdS geometries. This case represents the first step towards understanding a fully invariant formalism for WN field theories and their holographic duals.
Warped conformal field theory as lower spin gravity

Directory of Open Access Journals (Sweden)

Diego M. Hofman

2015-08-01

Full Text Available Two dimensional Warped Conformal Field Theories (WCFTs may represent the simplest examples of field theories without Lorentz invariance that can be described holographically. As such they constitute a natural window into holography in non-AdS space–times, including the near horizon geometry of generic extremal black holes. It is shown in this paper that WCFTs posses a type of boost symmetry. Using this insight, we discuss how to couple these theories to background geometry. This geometry is not Riemannian. We call it Warped Geometry and it turns out to be a variant of a Newton–Cartan structure with additional scaling symmetries. With this formalism the equivalent of Weyl invariance in these theories is presented and we write two explicit examples of WCFTs. These are free fermionic theories. Lastly we present a systematic description of the holographic duals of WCFTs. It is argued that the minimal setup is not Einstein gravity but an SL(2,R×U(1 Chern–Simons Theory, which we call Lower Spin Gravity. This point of view makes manifest the definition of boundary for these non-AdS geometries. This case represents the first step towards understanding a fully invariant formalism for WN field theories and their holographic duals.
Unification of Quantum and Gravity by Non Classical Information Entropy Space

Directory of Open Access Journals (Sweden)

Davide Fiscaletti

2013-09-01

Full Text Available A quantum entropy space is suggested as the fundamental arena describing the quantum effects. In the quantum regime the entropy is expressed as the superposition of many different Boltzmann entropies that span the space of the entropies before any measure. When a measure is performed the quantum entropy collapses to one component. A suggestive reading of the relational interpretation of quantum mechanics and of Bohm’s quantum potential in terms of the quantum entropy are provided. The space associated with the quantum entropy determines a distortion in the classical space of position, which appears as a Weyl-like gauge potential connected with Fisher information. This Weyl-like gauge potential produces a deformation of the moments which changes the classical action in such a way that Bohm’s quantum potential emerges as consequence of the non classical definition of entropy, in a non-Euclidean information space under the constraint of a minimum condition of Fisher information (Fisher Bohm- entropy. Finally, the possible quantum relativistic extensions of the theory and the connections with the problem of quantum gravity are investigated. The non classical thermodynamic approach to quantum phenomena changes the geometry of the particle phase space. In the light of the representation of gravity in ordinary phase space by torsion in the flat space (Teleparallel gravity, the change of geometry in the phase space introduces quantum phenomena in a natural way. This gives a new force to F. Shojai’s and A. Shojai’s theory where the geometry of space-time is highly coupled with a quantum potential whose origin is not the Schrödinger equation but the non classical entropy of a system of many particles that together change the geometry of the phase space of the positions (entanglement. In this way the non classical thermodynamic changes the classical geodetic as a consequence of the quantum phenomena and quantum and gravity are unified. Quantum
Matrix De Rham Complex and Quantum A-infinity algebras

Science.gov (United States)

Barannikov, S.

2014-04-01

I establish the relation of the non-commutative BV-formalism with super-invariant matrix integration. In particular, the non-commutative BV-equation, defining the quantum A ∞-algebras, introduced in Barannikov (Modular operads and non-commutative Batalin-Vilkovisky geometry. IMRN, vol. 2007, rnm075. Max Planck Institute for Mathematics 2006-48, 2007), is represented via de Rham differential acting on the supermatrix spaces related with Bernstein-Leites simple associative algebras with odd trace q( N), and gl( N| N). I also show that the matrix Lagrangians from Barannikov (Noncommutative Batalin-Vilkovisky geometry and matrix integrals. Isaac Newton Institute for Mathematical Sciences, Cambridge University, 2006) are represented by equivariantly closed differential forms.
Feynman's Operational Calculi: Spectral Theory for Noncommuting Self-adjoint Operators

International Nuclear Information System (INIS)

Jefferies, Brian; Johnson, Gerald W.; Nielsen, Lance

2007-01-01

The spectral theorem for commuting self-adjoint operators along with the associated functional (or operational) calculus is among the most useful and beautiful results of analysis. It is well known that forming a functional calculus for noncommuting self-adjoint operators is far more problematic. The central result of this paper establishes a rich functional calculus for any finite number of noncommuting (i.e. not necessarily commuting) bounded, self-adjoint operators A 1 ,..., A n and associated continuous Borel probability measures μ 1 , ?, μ n on [0,1]. Fix A 1 ,..., A n . Then each choice of an n-tuple (μ 1 ,...,μ n ) of measures determines one of Feynman's operational calculi acting on a certain Banach algebra of analytic functions even when A 1 , ..., A n are just bounded linear operators on a Banach space. The Hilbert space setting along with self-adjointness allows us to extend the operational calculi well beyond the analytic functions. Using results and ideas drawn largely from the proof of our main theorem, we also establish a family of Trotter product type formulas suitable for Feynman's operational calculi
Network geometry with flavor: From complexity to quantum geometry

Science.gov (United States)

Bianconi, Ginestra; Rahmede, Christoph

2016-03-01

Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but
Electric Chern-Simons term, enlarged exotic Galilei symmetry and noncommutative plane

International Nuclear Information System (INIS)

Olmo, Mariano A. del; Plyushchay, Mikhail S.

2006-01-01

The extended exotic planar model for a charged particle is constructed. It includes a Chern-Simons-like term for a dynamical electric field, but produces usual equations of motion for the particle in background constant uniform electric and magnetic fields. The electric Chern-Simons term is responsible for the noncommutativity of the boost generators in the 10-dimensional enlarged exotic Galilei symmetry algebra of the extended system. The model admits two reduction schemes by the integrals of motion, one of which reproduces the usual formulation for the charged particle in external constant electric and magnetic fields with associated field-deformed Galilei symmetry, whose commuting boost generators are identified with the nonlocal in time Noether charges reduced on-shell. Another reduction scheme, in which electric field transmutes into the commuting space translation generators, extracts from the model a free particle on the noncommutative plane described by the twofold centrally extended Galilei group of the nonrelativistic anyons
Clifford algebras, noncommutative tori and universal quantum computers

OpenAIRE

Vlasov, Alexander Yu.

2001-01-01

Recently author suggested [quant-ph/0010071] an application of Clifford algebras for construction of a "compiler" for universal binary quantum computer together with later development [quant-ph/0012009] of the similar idea for a non-binary base. The non-binary case is related with application of some extension of idea of Clifford algebras. It is noncommutative torus defined by polynomial algebraic relations of order l. For l=2 it coincides with definition of Clifford algebra. Here is presente...
Euler Polynomials and Identities for Non-Commutative Operators

OpenAIRE

De Angelis, V.; Vignat, C.

2015-01-01

Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt, expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, due to J.-C. Pain, links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Fig...
Scaling Limit of the Noncommutative Black Hole

International Nuclear Information System (INIS)

Majid, Shahn

2011-01-01

We show that the 'quantum' black hole wave operator in the κ-Minkowski or bicrossproduct model quantum spacetime introduced in [1] has a natural scaling limit λ p → 0 at the event horizon. Here λ p is the Planck time and the geometry at the event horizon in Planck length is maintained at the same time as the limit is taken, resulting in a classical theory with quantum gravity remnants. Among the features is a frequency-dependent 'skin' of some ω/ν Planck lengths just inside the event horizon for ω > 0 and just outside for ω < 0, where v is the frequency associated to the Schwarzschild radius. We use bessel and hypergeometric functions to analyse propagation through the event horizon and skin in both directions. The analysis confirms a finite redshift at the horizon for positive frequency modes in the exterior.
Kohn condition and exotic Newton-Hooke symmetry in the non-commutative Landau problem

International Nuclear Information System (INIS)

Zhang, P.-M.; Horvathy, P.A.

2012-01-01

N “exotic” [alias non-commutative] particles with masses m a , charges e a and non-commutative parameters θ a , moving in a uniform magnetic field B, separate into center-of-mass and internal motions if Kohn's condition e a /m a =const is supplemented with e a θ a =const. Then the center-of-mass behaves as a single exotic particle carrying the total mass and charge of the system, M and e, and a suitably defined non-commutative parameter Θ. For vanishing electric field off the critical case eΘB≠1, the particles perform the usual cyclotronic motion with modified but equal frequency. The system is symmetric under suitable time-dependent translations which span a (4+2)-parameter centrally-extended subgroup of the “exotic” [i.e., two-parameter centrally-extended] Newton–Hooke group. In the critical case B=B c =(eΘ) −1 the system is frozen into a static “crystal” configuration. Adding a constant electric field, all particles perform, collectively, a cyclotronic motion combined with a drift perpendicular to the electric field when eΘB≠1. For B=B c the cyclotronic motion is eliminated and all particles move, collectively, following the Hall law. Our time-dependent symmetries are reduced to the (2+1)-parameter Heisenberg group of centrally-extended translations.
Differential geometry of group lattices

International Nuclear Information System (INIS)

Dimakis, Aristophanes; Mueller-Hoissen, Folkert

2003-01-01

In a series of publications we developed ''differential geometry'' on discrete sets based on concepts of noncommutative geometry. In particular, it turned out that first-order differential calculi (over the algebra of functions) on a discrete set are in bijective correspondence with digraph structures where the vertices are given by the elements of the set. A particular class of digraphs are Cayley graphs, also known as group lattices. They are determined by a discrete group G and a finite subset S. There is a distinguished subclass of ''bicovariant'' Cayley graphs with the property ad(S)S subset of S. We explore the properties of differential calculi which arise from Cayley graphs via the above correspondence. The first-order calculi extend to higher orders and then allow us to introduce further differential geometric structures. Furthermore, we explore the properties of ''discrete'' vector fields which describe deterministic flows on group lattices. A Lie derivative with respect to a discrete vector field and an inner product with forms is defined. The Lie-Cartan identity then holds on all forms for a certain subclass of discrete vector fields. We develop elements of gauge theory and construct an analog of the lattice gauge theory (Yang-Mills) action on an arbitrary group lattice. Also linear connections are considered and a simple geometric interpretation of the torsion is established. By taking a quotient with respect to some subgroup of the discrete group, generalized differential calculi associated with so-called Schreier diagrams are obtained
Newtonian cosmology with a quantum bounce

Energy Technology Data Exchange (ETDEWEB)

Bargueno, P.; Bravo Medina, S.; Nowakowski, M. [Universidad de los Andes, Departamento de Fisica, Bogota (Colombia); Batic, D. [University of West Indies, Department of Mathematics, Kingston 6 (Jamaica)

2016-10-15

It has been known for some time that the cosmological Friedmann equation deduced from general relativity can also be obtained within the Newtonian framework under certain assumptions. We use this result together with quantum corrections to the Newtonian potentials to derive a set a of quantum corrected Friedmann equations. We examine the behavior of the solutions of these modified cosmological equations paying special attention to the sign of the quantum corrections. We find different quantum effects crucially depending on this sign. One such a solution displays a qualitative resemblance to other quantum models like Loop quantum gravity or non-commutative geometry. (orig.)
Thermodynamics of noncommutative high-dimensional AdS black holes with non-Gaussian smeared matter distributions

CERN Document Server

Miao, Yan-Gang

2016-01-01

Considering non-Gaussian smeared matter distributions, we investigate thermodynamic behaviors of the noncommutative high-dimensional Schwarzschild-Tangherlini anti-de Sitter black hole, and obtain the condition for the existence of extreme black holes. We indicate that the Gaussian smeared matter distribution, which is a special case of non-Gaussian smeared matter distributions, is not applicable for the 6- and higher-dimensional black holes due to the hoop conjecture. In particular, the phase transition is analyzed in detail. Moreover, we point out that the Maxwell equal area law maintains for the noncommutative black hole with the Hawking temperature within a specific range, but fails with the Hawking temperature beyond this range.
On Some Isomorphisms between Bounded Linear Maps and Non-Commutative Lp-Spaces

Directory of Open Access Journals (Sweden)

E. J. Atto

2014-04-01

Full Text Available We define a particular space of bounded linear maps using a Von Neumann algebra and some operator spaces. By this, we prove some isomorphisms, and using interpolation in some particular cases, we get analogue of non-commutative Lp spaces.
Noncommutative configuration space. Classical and quantum mechanical aspects

OpenAIRE

Vanhecke, F. J.; Sigaud, C.; da Silva, A. R.

2005-01-01

In this work we examine noncommutativity of position coordinates in classical symplectic mechanics and its quantisation. In coordinates $\\{q^i,p_k\\}$ the canonical symplectic two-form is $\\omega_0=dq^i\\wedge dp_i$. It is well known in symplectic mechanics {\\bf\\cite{Souriau,Abraham,Guillemin}} that the interaction of a charged particle with a magnetic field can be described in a Hamiltonian formalism without a choice of a potential. This is done by means of a modified symplectic two-form $\\ome...
Samples of noncommutative products in certain differential equations

International Nuclear Information System (INIS)

Legare, M

2010-01-01

A set of associative noncommutative products is considered in different differential equations of the ordinary and partial types. A method of separation of variables is considered for a large set of those systems. The products involved include for example some * products and some products based on Nijenhuis tensors, which are embedded in the differential equations of the Laplace/Poisson, Lax and Schroedinger styles. A comment on the *-products of Reshetikhin-Jambor-Sykora type is also given in relation to *-products of Vey type.
Constraints on effective Lagrangian of D-branes from non-commutative gauge theory

International Nuclear Information System (INIS)

Okawa, Yuji; Terashima, Seiji

2000-01-01

It was argued that there are two different descriptions of the effective Lagrangian of gauge fields on D-branes by non-commutative gauge theory and by ordinary gauge theory in the presence of a constant B field background. In the case of bosonic string theory, however, it was found in the previous works that the two descriptions are incompatible under the field redefinition which relates the non-commutative gauge field to the ordinary one found by Seiberg and Witten. In this paper we resolve this puzzle to observe the necessity of gauge-invariant but B-dependent correction terms involving metric in the field redefinition which have not been considered before. With the problem resolved, we establish a systematic method under the α' expansion to derive the constraints on the effective Lagrangian imposed by the compatibility of the two descriptions where the form of the field redefinition is not assumed
New effective coupled F({sup (4)}R, φ) modified gravity from f({sup (5)}R) gravity in five dimensions

Energy Technology Data Exchange (ETDEWEB)

Madriz Aguilar, Jose Edgar [Centro Universitario de Ciencias Exactas e ingenierias (CUCEI), Universidad de Guadalajara (UdG), Departamento de Matematicas, Guadalajara, Jalisco (Mexico)

2015-12-15

Using some ideas of the Wesson induced matter theory, we obtain a new kind of F({sup (4)}R, φ) modified gravity theory as an effective four-dimensional (4D) theory derived from f({sup (5)}R) gravity in five dimensions (5D). This new theory exhibits a different matter coupling than the one in BBHL theory. We show that the field equations of the Wesson induced matter theory and of some brane-world scenarios can be obtained as maximally symmetric solutions of the same f({sup (5)}R) theory. We found criteria for the Dolgov-Kawasaki instabilities for both the f({sup (5)}R) and the F({sup (4)}R, φ) theories. We demonstrate that under certain conditions imposed on the 5D geometry it is possible to interpret the F({sup (4)}R, φ) theory as a modified gravity theory with dynamical coefficients, making this new theory a viable candidate to address the present accelerating cosmic expansion issue. Matter sources in the F({sup (4)}R, φ) case appear induced by the 5D geometry without the necessity of the introduction of matter sources in 5D. (orig.)

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